Are you on the edge of a 4G area, or somewhere that there's weak 4G signal?
With my first few days with the S3, I didn't get a 4G signal at all in an area on the edge of 4G coverage where my MAXX, Rezound, Nexus, Bionic, and Charge all got 4G about half the time (although the Nexus and the Charge dropped signal constantly). I was worried that something was wrong with the phone. I then was finally able to get into an area with strong 4G, and it picked up 4G just fine.
In my experience, in areas of weak 4G, the S3 opts to stay with 3G in order to try to avoid constantly dropping the 4G signal (the Nexus and the Charge were always dropping 4G, as well as 3G, for me). My guess is that this was a conscious choice in an effort to maintain a steady connection. With the
Phone Info app, you can easily force your S3 into LTE-only mode. I did this when I was worried that 4G wasn't working, and in the weak area I was in, it connected to 4G. But the reception was quite poor, with 4G cutting in and out constantly. I could then see why the phone was opting to stick with 3G, and that helped put my mind at ease a bit.
The reception on the S3, like the reception on all Samsung devices in my experience, isn't as strong as devices from some other manufacturers. I think in the design process, Samsung was aware of that, so the phone is set to stick with 3G if the 4G signal is weak in order to provide a more consistent experience. In areas of strong 4G, I haven't had any issues with it dropping back to 3G.
