So I was having this problem with my wifi connection on my S3. It would disconnect for about 1 second then immediately reconnect. Getting the notification I was connected to my network every few seconds was getting really annoying. I searched all over the internet for an answer and I tried going into service mode and turning off power saving mode, that didn't help. I tried a factory reset, nope. Then I decided to try something that I did to fix a connectivity problem with my iPhone 4 way back when. I logged into my router and I changed the wifi channel from 10 to 9. And it worked! Granted I only did it about 10 minutes ago, but since I did it my S3 hasn't disconnected once. I'll report back if this turns out to not be a permanent fix.