Pheace: There appears to be an issue where people lose their non-steam games in the library sometimes. I personally have only had it happen with games I added, and where I didn't shut down the client properly. I'd suggest adding the games, then closing your client and restarting it to make sure it saves it to the cloud

Not sure why it would reliably remove it every few days like that though, unless you perhaps only reboot every few days and you let Steam shut down with windows (which tends to cut off it's shutdown procedure before it's done, so that might mess up your non steam games)