The copy of OmniFocus 1.10 available on our site did not work properly on 10.4, 10.5, and 10.6. It caused a keychain prompt every time the app attempted to sync.
We've fixed the issue, and posted a new version (1.10.1) in the usual places.
http://www.omnigroup.com/products/omnifocus/
The keychain will still prompt the first time you run the new version, because it's a new version. But after that, it should just sync silently, like it used to.
Sorry for the nuisance.
If you missed the 1.10 release notes, you can check them here:
http://forums.omnigroup.com/showthread.php?t=23703
(There will be no MAS 1.10.1 because this issue had no impact on Mac App Store customers.)