I've looked into this problem a couple of times. The last change we made to try to fix this was on Feb. 24th, change log entry here
(Admins Only). It was to put a period before the domain name for cookies. The cookies may be corrupted. They have the prefix phpbb3_m8j8i. In Firefox you can delete specific cookies, you could try to delete cookies with that prefix and see if that helps. I found 3 cookies with that prefix on my PC; phpbb3_m8j8i_u, phpbb3_m8j8i_k, & phpbb3_m8j8i_sid.
The other possible solution was to set the Security settings 'Session IP validation' to 'none' which it currently is set to. Supposedly for some Internet users their IP address can change while they're log on and this change was supposed to ignore that.
I don't what else to do with this random logout problem.
Rufus, you're probably talking about MySQL errors. These occur when the host (Bluehost) is performing backups or MySQL database maintenance. They usually do this late at night, around 2 AM US Eastern time. The only thing you can do is wait awhile.