I have the same issue with my Air and one of my email addresses, not both. I have tried everything and its really annoying to see my Iphone have no issues, same settings, etc and Ipad have this periodically. I spent time with several support people for my ISP and we never resolved it from their end--i do think turning wifi off and on again did the trick but not completely sure.
Today I had the issue again, only on the Ipad as before, iphone received without a hitch. I did a reset, deleted the account finally and did another reset but when I went to settings the account remained (?) but when the email client tried to download email it asked for my password and accepted it this time. I expect the poster had the same experience I had of being able to send email from the email address but just couldn't receive.
I did not have the same problem with my Ipad One or Three--I did have some wifi issues with both which required a reset of the (older) router but after purchasing an Airport Express the wifi issue didn't occur again. I believe its an Air issue--otherwise it seems that the Iphone would have shown the same message. I find similar complaints on the Apple ipad forums. Perhaps IOS 8 will resolve it. In the meantime, try all the suggestions and hopefully one of them will be your answer for now.
Nonetheless, I still really like my Air and am able to do almost everything on it--a bit more than Tim Cook at his 80% LOL. With each iteration of the Ipad from the One on and the upgrades in OS and increasingly terrific apps the Ipad is approaching being almost all I need. I had a quite powerful PC built for me 18 mos. ago but I'm guessing its the last PC I own and I've not replaced my laptop. I have high hopes that eventually I will be able to use Photoshop and Lightroom on an Ipad--perhaps the rumored larger screen Ipad Pro and right now I can do almost all my Office needs also on the Ipad with few exceptions.