I know this is listed a few times, but couldn't find where anyone posted a solution.
The Issue: I recently experienced the following issue whenever attempting to backup a site. The backup logs would always contain the following error,
"WARNING: Database error Cannot load from mysql.proc. The table is probably corrupted for query"
Coincidentally, I was also experiencing a dashboard issue and could not stay logged in for any random length of time.
The Solution: The thread link below is the solution on how I resolved both the Database Corrupt error that BackWPUp was spitting out as well as a session or logging out issue with the dashboard.
http://wordpress.org/support/topic/cannot-stay-logged-into-dashboard
Hopefully this will save you some effort. Cheers!