Hi everyone, first-time poster. I came across this thread after searching for issues regarding tethering on the GS3. Yep, I have the same problem.
I bought an unlocked international handset from Amazon UK and have been using it with a three UK PAYG SIM. This SIM and account worked great on my older GS1 and I never experienced any tethering issues, managing to support a laptop and two iPads at once.
But now on the GS3 the internet access is intermittent when tethering over Wifi. Sometimes it works fine for hours, but at other times it goes on and off every few minutes. Like others here the Wifi connection between the handset and device remains active - it's the actual internet packets which just stop being passed through.
I'm using WPA2 security. Sometimes switching wifi off on the laptop and back on again seems to start the connection again, but it may not last long.
So I don't have any decent solutions, but I wanted to let you know there's another person here experiencing the same issues, so any suggestions are very gratefully received!
Shame as I love everything else about the handset...
Gordon