Like the others before me, I am having the identical problem that the OP is having. I even contacted my mobile service provider tech support to see if they had any information about this, or had been given some kind of heads-up that iCloud was no longer going to work with the Android email app. I am running Jelly Bean (4.1.2) on a Galaxy SII. I did all of the troubleshooting things that I (and my provider's tech support) could think of; Tried to reset password, that failed. Tried sending test email to iCloud using another email client and checking iCloud.com in browser, that worked fine. Tried removing accout from Android email app. and starting from scratch, that failed, even after clearing the email app data in the application manager. Tried using TLS instead of SSL, that just sat and spun its wheels. Never authenticated. Up to today, I have had zero problems accessing my iCloud email using the Android email app. for over 18 months. Then today... well, you know the rest. I am not an IT guy, but it looks to me like something must have changed on the iCloud server side. Either by desing or otherwise.
As has been said before, I suppose that there is some consolation knowing that I am not alone, but this is pretty damned inconvenient and frustrating.
KC