Password Issue when attempting to enable Back to My Mac in iCloud Preferences - HELP?

Since upgrading to Mountain Lion, I have a problem enabling Back to My Mac. When I try and enable B2MM in the iCloud preferences window, I am asked to enter my Apple ID password. It says the password is incorrect, even though it IS 100% correct. I've even tried resetting my password (so that the password lives up to the latest security requirements for passwords, etc). So, it's definitely correct, and I'm able to login to my Apple account here (on this Apple laptop as well as on my iPad and iPhone)... it's not an issue when I log in anywhere else... I am only told my password is incorrect when attempting to enable Back to My Mac in the iCloud preferences pane.

Help?

Many thanks!