Thanks for providing a log. It was very helpful.
Whenever you run the game, Knossos updates the timestamp for when you last played that specific mod. The log says that Knossos is getting a "permission denied" error when it tries to update the relevant file in your Knossos library folder.
The example from your log is for Inferno:
Can you check if this file exists? Open Windows Explorer, paste D:\Games\Knossos\FS2\Inferno-1.0.0 into the address bar, press Enter, and check if the file user.json is there.
If the file does exist, is there some reason why Knossos would not have permission to access it?
You can try running Knossos as administrator, although I'm not sure that should be necessary.