Not sure if this is your specific problem - but one thing I've found that kills this phone fast is bad 4G cell reception. By default the phone runs as LTE/GSM/WCDMA (Auto) in Settings->Mobile Networks . If you are in a location with patchy (or none at all) 4G Coverage, the phone wastes an inordinate amount of juice switching to high-power mode on the cell radio searching for the elusive 4G/LTE ... Just like a 3G phone will deplete its battery extremly fast in a location with no/poor 3G connectivity (inside the 'secure' datacentres I wander into occasionally that have cell blockers, I can deplete the battery in a phone in about 3 hours just due to it constantly switching to high-power 'cell search' mode as it has no details on any cells to 'hand off' to....)
The difference is palpable... inside my office, if I have the phone on the right side of my desk closest to some windows, it will receive 'patchy' 4G and I'll go through about 60% battery over about 8-10 hours with intermittent phone use (most of the battery goes to screen time as I'm a 'fiddler' whenever I leave my desk for a coffee/break/etc...) If I place it on the left side of my desk, where the reception is much worse, it'll fall back to 3G and I'll go through about 80% battery doing nothing different...
I'm now in the habit of switching the phone to WCDMA Only when I'm going to be working in the bowels of the building, as there aint no hope of 4G there...Doing this drastically improves battery life.. Likewise if I'm stuck at home over the weekend, I leave it on WCDMA, as where I live has very patchy 4G as well and I only get it if I walk outside and down the street...
Just a possible reason for the excessive drain... at least worth trying anyway... *shrug*
Samsung Galaxy S3 (GT-i9300)