Sorry to bump this thread, but I am having the same issue with my rooted Sprint S3. It has never done this crap to me ever since I got it about 11 months ago. With wifi enabled, sometimes it would connect, most of the time it would not connect to my wifi so it would just stay on 3G. My Galaxy Tab 3 and my laptop are staying connected so its not the modem. Anyone got a solution to this problem?
It could still be your router. We had a similar situation in our house. Just to set up, we have the following devices connected to the WiFi Router:
- My phone (GS3)
- Wife's phone (GS3)
- My tablet (N7)
- Wife's tablet (Kindle Fire)
- DVD Player (Sony)
- Chromecast
Our problems started with the Wife's phone. It just kept dropping WiFi. Everything else was fine. We had to keep restarting her phone, and sometimes that wouldn't work. Then it started happening to her Kindle Fire and the DVD player. My phone, tablet, and Chromecast were all staying connected with no problems. I started to think she screwed something up with her devices. Then I noticed they were dropping at the same time. Then it started happening to the Chromecast. At this point, I started to suspect the WiFi router, but all along, my GS3 was perfect. No disconnections ever. Then the AT&T 4.1.2 update came out. As soon as I updated, my phone refused to stay connected, too.
I got a new router, and everything has been perfect since. The weird thing is that my Nexus 7 never had the issue. Its connection was rock solid the entire time. But everything else started dropping off...but the started at different times.
So my point is that WiFi routers can be weird and fickle. It's definitely possible that it's affecting only one device now. I'd try brining the device to other places and seeing if it connects. If so, it's most likely the router. If not, then it's most likely a device issue.
One thing, when the router would dump some of the devices, simply restarting the router fixed the problem for a few days. So try that first.