I hadn't touched my HTTPS plugin, but suddenly the website began acting strangely (homepage accessible only with HTTPS, etc.) After submitting a support ticket with my web host, I thought I'd take a look at HTTPS -- and lo and behold, the "Force SSL Exclusively" item had unchecked itself!
I checked the Force SSL checkbox again and then all was ok. This was a little spooky though. Does it make any sense that this could happen? Is there any way of making sure it doesn't happen again?