Applications :: Mac Mail Keeps Asking For My Password

For one of my e-mail accounts, Mac Mail will randomly give me a popup asking for the password for one of them (it gives me the option to save the password in the keychain). I've opened keychain access before and removed all of the entries for that account, and then that popup might show up once and i'll save the password and then things are fine for a while. But I've done this a number of times and that popup still shows up whenever it wants to! I've also removed the passwords from Mail's account settings, saved, and then put the passwords back in (smtp and pop). Doesn't work.