I regularly find PC getting very slow right around this time. I don't know the real reason but I've been assuming that something was busy doing nightly backups, indexing, archiving or other maintenance.

It's very similar to what would happen at another site where I used to participate. There, for example, a member could "kill" their own account without any help from the host or admins but the account would stay in "killed" mode (for any member to see) for up to 24 hours. Then, right around midnight server time, there'd be an obvious slowdown, all the killed accounts would disappear, and (as I recall) other updates to the database would also take place. Those slowdowns obviously represented scheduled database maintenance and that's why I'm guessing that ours might, too.