mail asks for password

I am continually asked for my password on my mail accounts when I do a new search for mail. I have tried the following:
1. put password in mail preferences and asked to put in keychain
2. changed password a couple of times
3. tried to do keychain first aid, but it won't take my response to password (the box shakes and looks at me) - not sure I know what I am doing
4. turned off and on computer many times
5. deleted and reinstalled mail accounts

Help, I am broken and can't fix it. Do I pay for Apple Care, go to store, return to Windows (ugh)
mjshack

How many mail accounts do you have and are they all with the same ISP? Try going to your ISP's mail server, log on, and change your password at the server. Then in Apple Mail change the password to be the same as you entered at the server. Make sure it gets saved in the keychain. Do that for all the accounts.

I have 2 mail accounts - Yahoo and at&t which has a yahoo address. The ISP is Uverse from at&t. I have changed my password at Yahoo. How do I tell if it is saved in keychain? When I go to keychain, find the password under login passwords entry to look, it tells me access is limited. When I go to keychain aid, verification is ok. Perhaps I don't understand what you are asking me to do.
mjshack