Does the site time out your user name?

I notice that from time to time, I have to log in again.

Yes. It is 3600 seconds, or 60 minutes.
I'm guessing that it is 60 minutes at being idle.
I have never been logged off, then again I don't think I've had phpBB open for more than an hour.

Do you check "Log me on automatically each visit:"?

If that's checked, you won't get kicked out