Q: Email now asks for password every time I try to access it.  Getting very annoying

you may want to try repairing your keychain and see if that resolves the issue, the following article tells how to do this:

http://support.apple.com/kb/TS1544

hopefully this helps, if not let us know

This happens to me from time to time. I've learned to just dismiss the dialog box by hitting cancel, and then hitting get mail from the affected account. Not bothered again after that.

Hi.

asking password if u try send/receive mail?

Do you look if they password are input in your servers(in/out) on Mail Preferences?

If not the Mail ill ask that every time you try send or receive a mail.

Strange...cuz he need to ask about password only to access any of outcoming/incoming server.

Try delete the line from your mail on keychain.

What is the version from your system?

I had this problem with outgoing e-mail.  The fix for me was to go to Mail-Preferences and check to see that the password is there for incoming.  For outgoing, click on the STMP for your e-mail account (be sure it is the same one for the highlighted account) and when you click on the arrows there is an "edit STMP" option.  CLick on that and hit Advance and be sure your password is in there.  Mine wasn't,so I just entered it and now it doesn't ask anymore.