Hi Tim, Thanks for your response. As you correctly said, being on a virtual host (GoDaddy) I'd hardly have access to php5.ini or setting memory levels. (Now what if Wordfence was using too much?) The odd thing though, is that the problem only affected the two sites that had Wordfence active, and that was the only changed variable on both (update on the 15th).
It could be a coincidence of course, as I have a couple other WordPress installations on the same host and they continued undisturbed. I deleted Wordfence, the cache folder and its files and all the MySQL tables and by coincidence the two sites returned to normal today.
Anyway, I turned logging on and will monitor to see what happens. I had only just a short time before blocked a range of IPs--from an Eastern European country--that Wordfence identified as attempting repeatedly to break in to the admin.
After I'm finished setting up the second site that had been affected, I'll reinstall Wordfence and see what happens.