Would you mind running First Aid on your keychain? You can do this via the Keychain Access menu. Before you run it, open preferences and make sure all the boxes are checked under First Aid.

Does that help at all? When you log into your account, the login keychain--assuming it's your default--should be unlocked.

There were no problems with the keychain.

Unlocking seemed to fix it, but it re-locks itself after a period of time. I notice that there's a preference to keep it unlocked, but it doesn't seem to do anything for me....

I'm gone for the weekend, so I won't be able to check anything.

I'm not sure why it's auto locking for you. Is your keychain and account password the same? First Aid should have repaired that but if they are different there may be problems...

(And by problems I mean extra authentication requests.)