said by kitsune:
2 step authentication shouldn't be the issue. When you remove the account on the mac make sure to remove it completely. including the ~/Library/Mail/V2/IMAP-*email address*(10.7 or later). Might want to check for a POP version of that folder in there as well. If it's the only account you might want to pull the com.apple.plist (10.6).
Ok did the cleanup - there was an old pop file there with a touch date from last year. I deleted that one.
Added both client accounts back in and all is working fine - go figure.....--
Nothin' left to do but smile smile smile