This doesn't solve the problem but the sync process for email accounts syncs or really transfers email account setup information only from your Mac to the iPhone so unless you have a new email account that you want to transfer the account setup information from your Mac to the iPhone or you have made a change to account setup information for an existing account on your Mac that is already available on the iPhone that you want transferred, there is no reason to continue syncing account setup information during the sync process.
Following NataoMac's post I went into Mail.app and made simple change (set junk mail delete to never.) Then quit prefs so it saved then went back and restored my previous setting.
Poof... all the mail accounts now show up again in the iPhone info page in iTunes!
Wow! I did the same thing, and it worked exactly the same way. I didn't even have to close mail or iTunes. The missing mail account just suddenly appeared where it was supposed to have been all along!