The database is shutdown each morning (4am GMT) for a complete backup, during which time the entire site is unavailable. It takes about 10 minutes.
As for the site being busy, it is! The new server was installed a year ago now and since then the number of users has grown still further.
However, a second server has been purchased and is being prepared. The combination will result in a significant increase in capacity.
PPRuNe is faster than most busy discussion forums because it is run on a top-grade infrastructure.
As someone else has eloquently said, if you want to support it, buy a title or some advertising.