I just got two new iPhone 5's the day they were released (9/21) for the president of my company as well as myself, both attached to our business account and our corporate Exchange 2007 server. My phone is also attached to my personal gmail account.
When replying to messages that came in through exchange, sometimes the message will get stuck "connecting" or "sending", and eventually (possibly 5 minutes later) the error message pops up simply stating that the message was unable to be sent. After that it sits in the outbox, occasionally retrying and failing in the same way until I finally delete it.
I had my gmail account setup using the gmail option, but last week I decided I wanted to get push notifications so I changed it so that the gmail account was using a Microsoft Exchange connection, and now that one fails as well.
If I turn the phone's airplane mode on and off, the servers will reconnect and the mail will go out, but if I don't do that, the messages that were hung up will remain so despite retrying periodically. Rebooting the phone also lets the messages go out, but sometimes within minutes, sometimes hours, the problem has returned. I have tried removing and readding the account, and on one of the phones I did a complete factory restore, and it didn't help.
I have all the latest updates in our Exchange server, and we have about 20 Android based phones and a few windows mobile phones that have no trouble at all.
Now that the gmail account (connected as exchange) is also having trouble, I can't help but think that it's either an iOS 6 problem or an iPhone problem, since I am experiencing it on two different brand new phones.