Gmail only keeps me signed in for a few hours, same with Facebook, then it signs me out. eBay is the same. When my husband ran the cleaner, did he wipe some key information needed to keep me signed in to my accounts? I am not accessing them from any other devices...
You probably need to enable the Cookies to Keep, see here how:
http://www.piriform.com/docs/ccleaner/ccleaner-settings/choosing-which-cookies-to-keep