Since Dragonhold dropped, the notification system for applications is bugged.
It used to give you a notification the second someone applied to one of the guilds, you have permission to accept / decline applications.
This doesnt work anymore.

Now you only get notifications for like 5% of the applications! They are still in the application window, but you have to check manually, which can be forgotten for a few hours. Maybe some Guildmasters / Officers don't even know this yet.

This can be a problem. There are lots of people who randomly apply to 10-15 Guilds and take the first ones. So you have to be lucky you see it to accept a potential new Member.

This is not a problem for "me", lots of other GMs i talked to have the same Issue.

Certainly it would be preferable to get a notification again.

ZOS knows there are Issues with it!

From the latest Patchnotes:

Guilds & Guild Functionality
Fixed an issue where accepting multiple Guild Finder applications could cause other applications to clear.

This was a slight inconvenience, but the bigger issue is still not touched / acknowledged.
I have written it in the "Bug-Report" section of this forum, i have written an ingame Bugreport (/bug).

All of it seemed to be ignored.

So if you apply to a Guild, and dont get a answer for days, the GMs or Officers probably didnt even see it. Because they got used to the notification.