It remembers the Gmail one just fine. I keep putting in the iCloud password in preferences and saving it. When I look again, the space is empty. I'm using Mail 7.0 in Mavericks. Anytime I quit Mail, when I reopen it again, it immediately prompts me to enter my iCloud password.
The solution appears in the February 2014 issue of MacWorld magazine. In Mail preferences, under the Accounts tab, choose the Advanced tab. In the authentication menu choose Apple Token.
This is a more detailed explanation of mikel31556 explanation above:
Open the Mail app. Go to Preferences. Click on the Accounts tab, and then the Advanced tab.
Look for the Authentication box. If you're having this problem, it will be set to "Password." Click on the box and select "Apple Token."
Apple uses Tokens as a secure way to access iCloud services without having to use your password, by providing your username and password to the app over an encrypted SSL connection.
Mail is no longer remembering my iCloud password.
