What do you mean? I wasnt aware that CC Cleaner was something that could be turned "On" and "off". Like it only runs when you run it.
Depending how you set the settings. IIRC If you leave the "stock" settings, it stays running in the background and will clear internet crap anytime a browser is closed.
Just humor me, cnrtl+alt+del go into task manager, end CC cleaner from applications and from the processes screen, then re try and see if it stays logged in.