A cursory glance at this forum has shown me, thankfully, that I'm not alone in this issue. Hopefully, it can be fixed with a blanket patch and isn't account specific.
Just in case it is, though, I'll give some specific details about my plight.
I have 2 accounts. One (@ Phoenix.Immortal) is associated with this forum account's email.
I play primarily on the EU server on both accounts, but also on the NA server of this account (my main). I seem to be having issues with not receiving tickets on my EU versions of my accounts.
On the first day, everything seemed to be going fine, and I received tickets across my main EU, main NA, and alt EU accounts for the activities (in that order).
The second day, however, was a different story. After not getting any ticket drops on my main EU account's main character, Kyliizra, from the Imperial City sewer bosses, I instead went to the Imperial City Prison dungeon. There were also no tickets in the chest after completing the final boss.
Thinking it may just be my character having the issue (which happened before during a previous ticket event--I had to use another character to receive tickets), I swapped characters and did the same dungeon. Again, no tickets.
(For the record: no, none of my accounts were at the ticket cap when this occurred; and, even if they were, the tickets should still have appeared as drops in the IC boss corpses or the dungeon chest.)
So, I then decided to move on to my main NA account and did the same dungeon there. Lo and behold, I got my 2 tickets from the chest.
Now, as I said, I did these activities on the first day in the order of: main EU, main NA, alt EU. So, if the ticket drops were on a timer, my main NA shouldn't have been reset if my main EU, by then, was not (I swapped servers immediately after my 2nd dungeon attempt on main EU yielded no tickets). All that aside, I'm pretty sure that the ticket drops reset at the daily reset time (2am Eastern US) anyway, making this whole timer speculation irrelevant. I did my activities around the afternoon Eastern US on the first day, and around the later afternoon on the 2nd day.
I then, a few hours later (but still well before the daily reset time), went through the ICP dungeon on my alt EU account, and... no tickets. I only tried my main character there.
So, if it's not the ticket capacity, or the timing, what is it? It's not an EU server issue (as I know plenty of people on EU who received their tickets), but, so far, this issue has only affected the EU versions of my accounts, but my main account NA was fine.
I am going to try more characters on my main EU account in the hopes that it works for one of them. Regardless of whether it does or not, though, I would encourage those of you who are having similar issues to this to continue to spread the awareness of it.