This has been happening to me for about a month........ I spend time typing an email or replying to one and hit send. The phone makes the swoosh sound as if it had sent; however, when i go to the "sent" box it is not there. In fact, it is no where to be found and the receiver never receives.
I currently have an iphone 5 and in the past have owned the 3g, 4, and 4s. I have 5 different emails with 3 different hosts (godaddy, and acenet being 2 out of the 3). The account setting have been the same for all 4 iphones i have owned and never had a problem; therefor, I highly doubt it is the settings. All 5 emails have the same problem on 3 different hosts; therefor, I doubt it is the host. i have no problems with the emails when using my laptop.
I contacted Apple last week about this problem along with several others. They set an appointment up for me at an Apple store and swapped my phone out. They also instructed me NOT to restore from backup, but rather setup and a new phone. I did that and I'm STILL having the same issues.
BTW, this does not happen ALL the time but rather off and on. It is beyond frustration to spend 20-30 minutes composing an email and sending to find out it has disappeared altogether.
So far I have confirmed that the issue occurs on WIFI, LTE and 4g. If i power cycle my phone then it appears to correct the problem for a while.
I contacted Apple today and spoke to "senior service support specialist" and he has never heard of this problem. He did; however, tell me he was going to elevate this to engineering to see if this is a problem they are aware of. I have yet to hear back.