And then the site went down for hours and hours after I fixed that.
(But thanks for the kind words and rep!)
In this latest case someone's Wordpress on our shared server got hacked on Sunday, and that overloaded the server and caused our own site to be unavailable. They suspended the offender and fixed the server. Unfortunately this seems to be a pattern with our host.
I'm still looking at transferring to a new host. Unfortunately you can't just copy everything to a new server and expect it to all to interact perfectly. I discovered this when I tried to move our current database onto our test server and found a whole host of problems. When I think we can transfer smoothly I'll look into making the move. I'll warn everyone when I'm planning to do it so you can plan for some disruptions while I get it all working smoothly.