Don't expect anyone else to have this one, but I was seeing drain on my 925 that was so heavy, it was losing 20% an hour WHILE ON THE WIRELESS CHARGER. Plugging in into wired, it'd charge, in about 5 hours.
Disabling apps, airplane mode, NFC off, location off, Bluetooth off, no change. Did a hard reset, and it was better until the next missed phone call.
Visual Voice Mail wasn't showing any new messages, but calling vm the old fashioned way revealed a message that came in EXACTLY when the problem started, yet never showed up in VVM.
Tried resyncing VVM, but it never completed, which I assume is the crux of this specific drain scenario, so I turned VVM off, and the phone immediately cooled and resumed a very slow discharge rate.
You'd think that airplane mode would have effectively stopped anything VVM would be doing with the radio, but it didn't, so I wonder if it isn't just some obscure CPU bound loop.