I have been using mod menu in my custom modpacks since forever, there basically isn't a single modpack it isn't in.
I find myself opening and closing its interface quite often, especially when doing the last tidbits of in-game configuration.
It would be nice if, either as a config option or default behavior, mod menu kept the last search result when you close in and out of its interface.
(In between restarts would also be nice to have, but that sounds like a big hassle for not much, unless the foundations are already there)