Mail keeps asking for my iCloud account password

If Mail keeps asking you for your iCloud email address, this is a sign that something goes wrong with the server configuration.

The easiest thing you can do is to delete and add the iCloud account again. Close Mail, open System Preferences > iCloud and untick Mail. Then, tick Mail and open the Mail application, and see if you can connect. If not, there may be a problem with the server

but it wont let me delete it it keeps asking me for a password to a old apple id ,that i already changed and password 3 x today but yet still saying wrong password

I too am having this problem for the last two days.... I have tried what you said mende1 to no resolve. I know that password is correct. but it just keeps asking me to resend it. Therefore I am not getting any email, nor can I send any email.

I was having the same problem and I found by opening mail preference and going to the iclound account then to advanced then click the drop down saying password I changed to apple token. All is working now and I am getting icloud mail. Hope that helps you as it fixed my issue

Fantastic, thank you spearguy! I've been having the problem since I upgraded to Maverick a few days ago and this has fixed it.

Thank you! It worked

Unticking mail and re-ticking it again in System Preferences > iCloud worked for me! Thank you!!

My S.O.'s iMac running SL keeps having this problem.

Funny thing is, her old PowerBook G4 running Tiger *always* works correctly.

Don't understand why, if the problem is "Apple's servers", she can access her mail from the PBG4 but not her iMac.

Thanks - unclicking System Preferences > iCloud > Mail worked for me also.

Thank you very much for a great tip. Got sick of having to continuously input password everytime I accessed Mail

Turn off keychain in settings and then turn it right back on. Worked immediately for me.