I had the exact same problem but with only around ~30 files that kept seeming to be deleted every time i launched the game from Steam, which meant elements of the game didn't work (e.g all text in-game said "#autoLOC####" or i had no contracts available in a fresh campaign etc.). Each time i did the 'Verify Integrity of Files' it brought them back, only to have them deleted again as i launched the game.
To fix it, i first made sure to do the 'Verify' thing to get all the proper files in place and then went to the games files through steam using the 'Browse Local Files' option in the games settings, and copied every single folder there to another location on my PC. I intentionally only copied folders, and left the others (txt files etc.). Then i launched the game again (knowing it wouldn't work as i hadn't made any changes yet) just to refresh the files and again the game wasn't working as expected.
Closed the game, deleted all the files in the game directory (the files i first copied) and then copied them back into their proper file location from the backups i had saved elsewhere on my PC.
Not sure exactly why this worked, but once i had put the files in there myself i didn't have any issues again. I don't know if this means the issue is on the KSP or the Steam side of things, but either way the files stopped getting deleted on launch once i did this.
Hope you get it sorted!