Mail repeatedly asks for passwords for Gmail and Mae.com with Snow Leopard

Since I have installed Snow Leopard, Mail now repeatedly asks me for passwords for my Gmail and Me.com webmail when retrieving messages. I have checked the Remember in Keychain box and have also gone to Preferences and typed in the passwords into the Mail setups but no luck. What's more, whenever I go back to Preferences in Mail, the password fields are always blank.

Any thoughts?