My hosting service admits that both the php memory and version of MySQL is outdated. I finally got to a tech support guy there who knew something about WordPress and he said he knows it is indeed one of those two situations (mentioned in the reply above) causing this issue.
He told me put in a request for upgrading but mentioned this would not happen soon so I am not upgrading WP on any of my other WP sites.
I now recommend vehemently that anyone who wants to host a WP blog stick with the hosting services recommended by WP! (This is a big ‘live and learn’ for me!)
Thanks for the guidance!
