Updated Outlook/Exchange password on work laptop, but new password not accepted on iPhone 5s

I was recently prompted to change my Outlook/Exchange password on my work laptop, and after updating the password on my iPhone I keep getting "Cannot verify account" and "Incorrect password" messages on my iPhone.  I know the credentials are correct, because I can access email on my work laptop and through the web browsers on my phone/computer.

This problem has been going on for almost 2 weeks - originally, I had an iPhone 4s (iOS6) but I have since upgraded to the iPhone 5s (iOS7).  I've tried deleting and re-adding the Exchange account several times, I've reset the phones (old 4s and new 5s), I've restored them both to factory settings and reinstalled everything, and just about every other fix I've found after days of searching on Apple.com and elsewhere on the web.  I've also taken the phones (both!) to the local Apple store several times and called Apple Care support.  

Nothing has worked so far, and this is now starting to affect my work - missing important emails and meetings.  Is there anything else you can suggest?

Thanks!