Currently Favorited gifs will disappear from your folder if you log out of discord. I reset my computer which logged me out so I lost all of them. The gifs should stay in the favorites folder unless we as the users remove them from their folder of the gif no longer exists.
A team Discord member (Karl) replied to my inquiry saying "logging out of your account will indeed reset your saved/favorited GIF and your settings ... I'm so sorry again that we don't have a current solution for you at this time, but I like to think that anything is possible in the future".