Firstly, make sure your mod library isn't located in some system protected folder (like Program Files). Software has notable difficulties saving any files in such places. Then check if you aren't running out of disk space, this obviously can also cause problems.
I have no other ideas why mods would just casually stop being detected by Knossos without the user touching anything inside their files. That said, Knossos detects the mods by them having a mod.json file in their directories, so if the file is missing or corrupt, the mod won't be detected (the latter is a known occurence for the people who modified the file to manually force different dependency versions - yes, you can do that just fine, it's a text file - and didn't use the correct syntax).
As for reinstalling said mods back, during installation, Knossos always checks for leftover files and whether they're valid. It will only re-download the missing or damaged files, basically. So for example, you can delete a mod's mod.json file, refresh Knossos and that mod will be missing - but if you install said mod from the Explore tab, it will download the mod.json and only check for existence and validity of all of the other files.
Currently Knossos can only "do one thing at a time", as in, install one mod at a time and it sometimes does cause issues with other functionality. I have had notable issues of "apply to all builds" and "save" in Knossos settings not working until a mod finishes installing. That said you do have control over how many files can be downloaded simultaneously, and you can set download speed limits. See Knossos settings -> Downloads.