When you upgrade to Apple's iCloud service from MobileMe, the system will transfer your Mail account over to the new service as well. While not much changes for Apple's Mail service itself, some people have found that e-mail clients such as Mail will sometimes not connect properly.
When the connection problems happen, Mail or other e-mail clients including those on iOS devices will issue a message stating something like, "The iCloud IMAP server 'p99-imap.mail.me.com' rejected the password..." and request that you re-enter the password. When you do the password does not work, and the message is shown again.
This appears to happen randomly, so an e-mail client may go for a while with perfect connections to the server and then suddenly show the problem.
This is likely a configuration issue on Apple's end with its iCloud servers, but if it happens to you there are a couple of things you can try:
- Quit and relaunch Mail
Sometimes just quitting and reopening Mail or your other e-mail client will stop this from happening, at least temporarily. Do not repeatedly enter your Mail password or delete the Mail password keychain entry, as these actions will just result in the same issue.
- Wait it out
Since this issue is likely rooted in Apple making adjustments to its iCloud service, it may be best to just wait it out. Sometimes the issue goes away immediately, but other times it may take a few minutes. In general, the problem seems to have been becoming less prevalent since iCloud's introduction.
- Change your iCloud password
If your password for MobileMe does not meet the password requirements for iCloud, then you might run into this issue. You can change or update your e-mail password at Apple's secure Apple ID password management page.