The problem is a failing HDD in the main server. It's using a RAID-1 array, so there are two harddrives duplicating every action. There's no chance of data loss, but when one HD fails the whole server goes catatonic and seizes up. It takes a manual reset to bring it back up, and I can't always count on zumi's mom to do it for me.
New HDD will be installed end of December.