I've got exactly the same problem with my iPhone 5 (32GB). I talked to the support over the phone and they offerd me to send it in for service. It ended up that I got an new iPhone 5. But the battery just drains for no reason. Talked to the support again, service ...again.
The apple-support tested to send me a diagnostics test. They coundn't see a problem.
After all test I've done myself, I think it is the cellular network that is the problem.
If I put the backside of the iPhone to my ear I hear a sound that is a very high tone. Then when I turned the cellular network of, it didn't sound at all. And the battery works just fine.
So maybe it could work if you tested a new nano sim.
Because, the service seems not to work, or as you said wait for an upgrade.