Can't change password/re-add Gmail account in Mail

I recently changed the password on one of my Gmail accounts, at which point the Mail app on iPhone said "cannot get mail" because the password was incorrect, as expected. When I try to reset the password in Settings, I can reenter the password successfully, but the page it returns to in Settings still says the password is incorrect. I then tried deleting the account and re-adding it, but it does not re-add the account after I enter the username and password, which is essentially the same problem as before. It is an academic account associated with my school but is still accessible through Gmail via Google Apps.