A friend (a real Mac Guru) suggested the following solution to me and it worked:
"Sounds like the address book is screwed up. I'm assuming you tried turning off sharing and any kind of syncing to see if that was causing it, but had little luck.
So the next step is to rebuild it. First things first, open Address Book and do an export of all your data. Make sure it's got a backup. Then quit address book. Then go into your user's home directory and Library folder. In Application Support rename the "address book" folder to something else (like Old address book). Go ahead and trash the plists again too.
Relaunch address book and see if it's empty. If it is, great. If not, then something is syncing with it. Check MobileMe preferences, missing sync, etc. If you still can't get it to stay empty, let me know and we'll look into cleaning out your sync preferences." (I didn't have to email him further.)
"Once it's an empty address book, let it run for a bit and see if the problem persists. If it doesn't (it's fixed) then re-import your data from the export file into the new (freshly made) address book. If the problem remains, then it's not the application support files and your address book data, but the program itself. You can delete the new "address book" folder from Application Support and return your old one to it's original name.
If it's the application then we need to reinstall the program - if you can get Pacifer you can use it to extract the pkg file to just reinstall Address book (it's on the OSX DVD), or you can reinstall the entire OS from the DVD."