This is happening to me as well, but I'm not seeing a drop in battery life at all. Remember, this phone is constantly going on about WiFi network availability. It could have something to do with some sort of signal "keep alive". Maybe it polls a small amount of data to maintain priority on the network?
Given my experience with the Galaxy Nexus battery life, I purchased a giant battery via Amazon for my SGS3 in the first 24 hours that I had the phone. It hasn't even arrived yet and I'm much happier with this phone. The stock battery is doing the same job that the extended battery on the GNex did. When I say extended battery on my GNex, I don't mean the 2000+ mAh garbage that the carrier tries to sell you. I went online and purchased a 3000+ mAh battery with a larger battery door that increased the thickness of my GNex two-fold.
Aside from Touchwiz, I'm very happy with this phone. I've resolved just about every qualm I had with Touchwiz (camera app, gallery app, sms / mms text size conflicting with the system font size, LED indicators, etc). I'm actually very happy.
A word of advice: Try the power saving feature that is built into the phone. With moderate use, I got 20+ hours with the factory battery. I never turn off 4G and I constantly have corporate mail sync enabled.