Introduction
So, something I had always been wondering was the possibility of sustaining simmering frenzy indefinitely.
Now, firstly it was a question of whether this was possible, and secondly if it was could such a build exist that may still be viable and hasn't simply given up too much just to sustain frenzy.

Preface 1: The purpose of this was more to see what was possible as a theorycraft experiment, rather than actually being a viable end game build. There are probably some actual game realities that limit this. (Testing this isn't really possible for me, I'm on Xbox so can't use PTS and I also don't have the gear or skills to test it properly)

Preface 2: This whole thing is theorycrafted based on the UESP Builder. It assumes a couple of things:
1) The way the cost reduction methods affect scaling cost of simmering frenzy on UESP builder is correct (I would expect this to be the case as it follows the general convention for other skills)
2) Whether or not there is an actual "cap" to simmering frenzy stacks. If there is, and we can reach and sustain it, then the build can effectively just operate at that cap. If there isn't then the build will instead have to re-toggle frenzy on when its cost reaches the total health (and hence can't even be paid for despite how much healing there is). In this case I would look at the average number of stacks (ie: half the maximum achievable) to assess the build. I have seen mention in a few places that simmering frenzy caps out at 99 or 100 (and builder itself only lets you put in up to 100), so this is the assumption I will be going with.

General approach for the build
Simmering frenzy adds damage and has increasing cost. Thus if the build can get to the point where that increased damage actually provides more healing than the increased cost, we can sustain it indefinitely. Increasing the healing relative to the cost can be achieved by:
- Cost reduction of the cost of simmering frenzy
- Multiplicative factors that effect healing from spell damage, including weapon/spell damage percentage buffs, critical chance and damage, and percentage healing modifiers. Of these the first two categories are preferred (damage and critical buffs) as these will also increase damage done, as well as healing.

From this point it is about finding suitable skills and rotation to heal and do damage. For the purpose of this theorycraft to keep it simple, rather than trying to come up with a rotation using heals and damage abilities, this process took the approach of using skills that heal for a percentage of damage done, in fact only one. This was improved through use of the new mythic, Ring of the Pale Order, although use of this may not actually be necessary (this build takes the approach to actually get surplus healing).

Build decisions

Race and Class selection
For race, basically only two races were considered, being Khajiit and Argonian. These are the only two races that provide a multiplicative effect to healing (either through crit or straight healing done). Of these, Khajiit was chosen as it also provides offensive benefit.

Class was a bit harder. Some of those considered were:
Nightblade offers may crit buffs and also healing done from passives, and a skill that heals from damage if magicka (swallow soul)
Sorcerer offers a percentage buff to spell/weapon damage, a damage buff for physical damage (helps if we heal from it), Amplitude, and Cost Reduction.
Templar offers crit damage, potentially healing buffs, and a skill that heals from damage if magicka (sweeps)

Of these Sorcerer ended up seeming to be the easiest to work with, as the cost reduction is very useful. A tipping factor was that I wanted a simple rotation, and Sorcerer could use pets for free damage while spamming other skills. One issue was that this didn't give a healing from damage skill, which basically pigeonholed the build into being stamina based and using Bloodthirst. (This actually ends up probably being better anyway, as stamina has better availability of weapon damage percentage buffs via fighters guild, better crit sets, and also better crit passives from DW)

Cost reduction
Cost reduction for simmering frenzy is achieved via
- Infused Tri-Cost reduction glyphs
- Vampire Stage 4
- Vampire Lord Set (Even though this is a magicka set, the cost reduction given by this is significant. May be possible to replace but the without the h/s increase may be too much)
- Sorcerer passive
With all of these, the starting cost of frenzy is 675 h/s. At 100 stacks (max in UESP) it is 14161 h/s.
(Note: Without Vampire Lord, it would be 916 h/s at the start and 19219 h/s at 100 stacks)

Other Gear
Firstly, the new Ring of the Pale Order seems almost mandatory, as this makes it much easier to avoid having to work heals into the rotation, and makes it much easier to overheal the cost of frenzy.

For the rest, Crit Chance and Crit Damage was the focus. One thing I was conscious of here is that if going for crit its actually important to get crit chance as close to 100% as possible, as if the build relies on crit for maintaining the heal there is a chance it would get an unlucky sequence of non-crits and not keep up with frenzy. So weapons chosen were dual wield precise daggers (in retrospect axe + dagger may be better given axe bleed scales with damage and could provide extra free damage and healing).

For the second set, sets like Tzogvin's, Leviathan, Berserking Warrior, and to a lesser extent Relequen fit this bill. Can't use Berserking Warrior as its heavy and weapons + jewellery is already used by Vampire Lord (which is light). Of these I currently have Tzogvin as gives the best of these, so I currently have that in the builder. Relequen is likely more damage though and would probably still be ok in having enough heals for frenzy.

All gear medium divines (except one divines light piece of Vampire Lord that gets displaced by the Ring of the Pale Order, optimal place for this is belt but I currently have it on shoulder as that makes it easier to swap body sets with builder) with Shadow Mundus.

Skills
To keep it simple I wanted to try to get this to work simply using one skill to damage and heal, in this case Bloodthirst.
This was for simplicity, but also because one other consideration for any rotation is that there can't be gaps in the heals, ie: you need heals every single second.
What this means: Its very difficult to fit a buff/utility skill into the rotation, as unless you have a HoT running to cover the heal for that GCD, the heal upkeep for frenzy won't be met. Which would then require adding HoTs to the rotation. And many of the HoTs are on a 2sec tick (like blood craze) which would mean it would become crucial that these get cast on alternating seconds. So instead I opted to avoid all that, and simply design around spamming Bloodthirst. As such the remaining skills were simply added based on what they brought as a passive. So fighters guild for weapon damage, and sorc pets for a slightly lesser damage, but also the pet which adds free damage (as they now scale with damage not just stat so they benefit from frenzy) and also a health bonus.

This resulted in
1) Bloodthirst
2) Bound Armaments
3) Twilight
4) Clannfear
5) any fighters guild skill (while force from trap would be helpful, can't afford to cast it as that would result in a gap in heals so instead I get it from Tzogvin, likewise savagery from hunter is also helpful, but covered by potions anyway)
U) Dawnbreaker of Smiting (the bonus from Flawless is minor, and the increased damage of Smiting means the build can actually afford to cast it and get enough heals from Ring ot the Pale Order to keep up with Frenzy)
Backbar (not really necessary but added for just to see if we could cover non-combat periods) is the same but replace Blood thirst and Bound Armaments with Vigor and Circle of Preservation - these two skills if cast on cooldown provide enough heals to keep up frenzy if there is a period where Bloodthirst can't be used (although you have one GCD to realise that, bar swap and start healing otherwise you'll lose frenzy)

Other stuff:
The build also includes some health bonuses so that there is a buffer between full health and the max cost of Frenzy. This is to give a bit of a buffer in case a hit is missed or something. Ideally, health would be double the max cost of frenzy, as this would mean it has a extra GCD to react in and swap to heals when necessary. This could be achieved by moving more points to health and changing enchants, but comes at a damage cost obviously.

Sustain may also be an issue. This is actually quite important as performing a HA may actually take too long and cause Frenzy heal upkeep to be lost. Could be helped by outside sources, restore stamina enchants or poisons etc.

CP
I haven't put in a full distribution in (only really cared about what was in the blue tree as well as quick recovery) and what is there isn't optimised. The only things out of the ordinary are: no thaumaturge (Bloodthirst is direct damage not DoT according to builder), and instead use blessed. It probably also needs some penetration.

Full build:
(note: Ring of the Pale Order isn't in there yet so I have just put a random ring in its place. Also note the builder is currently in a state where some things have been updated for markath, but others haven't)
https://en.uesp.net/wiki/Special:EsoBuildData?id=278217

Result (at 100 stacks of Frenzy):
Frenzy cost: 14161 h/s
Bloodthirst tooltip: 27430 (11786 for last hit, which heals for 63%)
LA: 12817

So just from tooltip values, LA + Bloodthirst would heal for the following every GCD
(note healing modifiers of 10% healing done and 15% healing received)
(note 2: I know this assumes a fully penetrated target, but also ignores vulnerability etc)
Ring healing from LA + Bloodthirst: (12817 + 27430)*0.15*1.1*1.15 = 7636
Bloodthirst last hit healing: 11786*0.63*1.1*1.15 = 9392
Total: 17028
After considering crit chance (80.2%) and crit damage (121%) (note: as healing comes from damage, it is crit damage not crit healing is the relevant stat):
Total: 17028*(1 + 0.802*1.21) = 33552
Maybe more, does the ring heal from pet damage?

So, assuming the rotation is exactly every second, the healing is sufficient even before crit, but the aim was to have significant surplus healing to make it easier to keep frenzy up in case you miss a LA or something.
Alternatively, this shows the build could actually sustain Frenzy without Vampire Lord, so dps could be higher by simply doing something like swapping to Tzogvin + Relequen. This just means there is less margin for error, and the health buffer is less. It also may not be possible to sustain the healing when not attacking as vigor + circle of preservation isn't quite enough in that case I think (haven't checked though)

General estimate of dps just from LA + Bloodthirst (assuming cast every second), by also including crit chance (80.2%) and crit damage (121%):
(12817 + 27430)*(1 + 0.802*1.21) = 79303
Plus whatever the pets do.
So its getting into the realm of actual reasonable dps, just by spamming one skill.

Conclusion
Still too early to really tell. Clearly it is theoretically possible to sustain frenzy. Whether this is actually possible in real gameplay is a totally different question. And whether its worth it also remains to be seen, and would rely a much more optimised approach than I have taken.

Very happy to take any thoughts, comments, suggestions, or for someone to take this idea and do some actual proper testing.
Just putting this concept out there in case it could actually become something more.