A lot of users at my company appear to be continually asked for their user name and password credentials when trying to retrieve emails (From Exchange) on their iPhones since updating to version 7.1.1
It looks like Apple have somehow screwed something up again!
A three point solution that seems to have fixed the vast majority of these cases within the company:
1) Delete the email account
2) Hold down the power and home button (as if you are taking a screenshot) until the Apple logo comes up (can be a good 10-15 seconds). Let go straight after seeing the Apple logo.
3) When restarted, re add the email account using your correct credentials
Please note from my testing, 50% of phones were fixed after just doing the reset as per step 2. For the ones where this didn't work, I added steps 1 and 3. There are still a few phones that won't save the password - I believe something else is the problem and if I find out, I'll update this post.... It is more than likely this will be stealthy fixed in a future update.
I tested this on:
Iphone 4, 5, 5s
Ios version 7.1.1
Connecting to Microsoft Exchange on premis, Office 365, Outlook.com