Mail app rejecting password

I have been using apple mail for a while now, I have 4 accounts on it (2 gmail accounts, 2 psmail accounts). All of a sudden yesterday both psmail accounts stopped sending and receiving emails, and apple mail started asking for my password. I am able to sign in to both accounts online, AND I am able to send and recieve emails via my ipod touch. So it seems to be a problem just with the mail app. Anyone have an idea about how to fix this?