When they are backing up the table it very well could be taxing MySQL heavily and contributing to the problem.

As for restoring a backup table. You could use something like phpmyadmin to drop the old table (not the entire database) and then import the backup table.

As this happened the last two Saturdays, I will do a backup of that table on Friday evening, or first thing Saturday morning, and, if it happens again, I will drop that table and import the backup one via phpmyadmin.