Here's one thread that found a fix for a few people...
WiFi issues disconnects etc (fixed for me)
I don't have an S3 yet but on DroidX the wifi will essentially disconnect when it hasn't been used for a while and then reconnect when I bring the phone out of sleep mode, which takes 30 seconds to a minute to reconnect. When my power control widget shows a muted green it is normally when something is in the process of turning on but is not fully powered up and connected yet (like wifi or blue tooth). Once the radio is on and connected the power widget indicator turns a brighter green. Maybe your wifi is going into power save mode and when you bring the phone out of sleep mode the wifi has not finished powering up and reconnecting to the router yet. Again, I don't have and S3 yet (still waiting for mine to arrive) so this could all be nonsense.
There was also another thread where someone said assigning a static IP to the phone helped.