How often are accounts automatically synced ?

Once a week I think.

Well.. I found out that some games stop working probably after some time, so having a lot of games installed itsn't really that great afterall, when they all stop working after a while

I believe every 10 days (got my profile private so I am forced to sync it manually once in a while).

Once a week, it even says so on the sync page.
"For those using a private or friends only profile, you'll be able to bring your account up-to-date by briefly switching to a public profile for a few seconds a week."