Well you have two possible problems.
The first relative to the S3 is that Samsung ships the thing with WiFi Power Save turned on which when it senses you have not used WiFi for a certain period of time, turns it off. I have posted several times how to turn that off.
The other issue is related to your routers. 802.11 wireless protocol has only three channels on the 2.4GHz band that do not overlap with other channels (1, 6, 11). I have a reasonable sized warehouse at work using Cisco Air Connects and we had issues with clients not switching between Access Points and we had 8 Access Points. By reducing the number to 3 and setting each on it's own fixed non overlapping channel then interference went down dramatically. We even had before and after coverage drawing made a consultant who reconfigured the wireless network for us. The 802.11g automatic channel stuff does not seem to work reliably. You might want to consider this.
Mike