According to Reuben Engel over at Tips and Tricks in Mavericks, there’s a potential bug floating around in the latest Mac OS X.
Some folks have been reporting that they have to enter an iCloud password each and every time they open the Mail app. This might be only the folks who used Mail prior to the upgrade, but if one of them is you, here’s a possible solution.
Launch Mail on your Mavericks-enabled Mac and click on the Mail menu. Select Preferences and let Mail open the prefs window.
Once there, click on the Accounts tab and choose the iCloud account in the list to the left. Next, click on the Advanced tab and look for Authentication. There, you’ll see Apple Token.
Here’s a possible to solution: open Mail, under “Mail” in the menu bar, look for Preferences -> click on the Accounts tab and select they iCloud account that is causing the problem. Then, select the Advanced tab and under Authentication, choose Apple Token from the pop-up menu there.
If that solves your problem–hooray! If not, let us know in the comments below and we’ll look around for any other fixes.
Source: Tips and Tricks in Mavericks