This issue is what I am facing after directly dealing with #758, which I faced _after_ the latest stable update. Here are the details.
Telegram Desktop seems to have a limit on the total number of sticker packs added to it (independent of the number of stickers in the pack). For me, this limit seems to be around 21 packs (_EDIT:_ 21 not 22) (including the default "Great Minds" pack). Upon trying to add more, I am faced with this error:
I can add another pack by _removing_ an already-added pack. This seems to create some "space" where I can add one more pack. I have verified this by removing two packs - this allows me to add two others.
The issue has only been present from today. Yesterday was when I got the latest update for the stable version. It was working perfectly fine till then. Today I see that some of my packs had disappeared as described in #758, and so I followed the above steps. However they led to this new error.
UPDATE: The error seems to exist in Telegram for Android as well, now that I logged back in and checked. It shows this _highly informative_ (/s) toast under the same circumstances:
It's a server limit: https://www.twitter.com/telegram/status/606457674558017536
Aaaand it's fixed!! Thanks for the help anyway. This scared the bricks out of me. I'll proceed to close this now.