I have the same problem and another one that is also reported here. My Elite flips work great with iPhone 4. But with iPhone 5, I have two units that echo back to the party on the other line, and one that will completely drop the audio mid stream and have to scramble for my phone and switch the source while the other party is talking away.
This has been since the introduction of the iPhone 5. I have been through four different Elite flips through Motorola, so I'm starting to see it isn't the headset, which worked great with my four. It must be the iPhone 5 bluetooth connection.
I have the exact same problem. Just got my iPhone 5 a few weeks ago. Used my Motorola Elite Flip with my Blackberry for the past year without any problems. Now, I lose audio, or I get the same buzzing noise like you described. I would love to figure this out, but I will likely have to move to a different headset.
After getting a second Motorola flip which had the exact same problem I gave the flip to my wife to use with her iPhone 4, absolutely no problem with it. It stopped working only because she put it in the wash in her jeans.
I bought a Plantronics M-50 and it works great.
Apple does not monitor these forums or they don't care to address the issues, I called Apple the only response is to the restore the iPhone 5 which is a pain in the rear. I have done it the past to no success so I ignore that piece of BS advice.