I too am having the exact same problem.
On May 30, I had this problem for the first time. I was on a phone call, when all of a sudden in the middle of the conversation, the other party couldn't hear me. After a few re-attempts to make the call 'work', we were able to complete the conversation over FaceTime without any issues.
For the next 2 days, my phone was a useless brick in my pocket. Skype/Evernote/Voice Recorder all work great, and I could hear the other end just fine. I rebooted, I restored from backup, my next step was going to be to take it to the Verizon store and leave AT&T..
The morning I was planning to visit the Verizon store to change networks and get a new phone, I received a phone call and the phone was working perfectly fine again. Baffled, I assumed the problem was solved.
Fast fwd to today (June 12) I was on a call this morning with my bank, and all of a sudden the other end couldn't hear me. I had the entire call on speakerphone, so I wasn't touching the device. I ended up having to end the call as the other party simply couldn't hear me at all. Every call I've tried to make for the last 5 hours, has resulted in the same problem: they can't hear me. I've been in different parts of LA all day, so I've been on different cell towers, so I don't think it's the network. Again, Skype/FaceTime/VoiceRecorder all work fine. There is clearly a defect with the phone app (or something running in the background that is causing a conflict of sorts) that is causing it to mute out our voices.