keychain access doesn't delete passwords

I'm having some trouble with my Mail account - it won't remember my password in the keychain, so every time I open Mail I have to reenter it. So I think the answer to this (?) is to delete it from Keychain Access and start again. So I've opened Keychain Access, and deleted that password, plus a whole load of other defunct passwords while I'm there. It seems to work okay, but then if I close Keychain Access then re-open it again, all those old passwords are sitting right there again, as if I hadn't done anything.

Help please?!