How to increase the amount of time the wifi waits before timing out a connection?
I doubt there's anything you can do short of jailbreaking and re-flashing the code that drives the wireless chipset.

The things you can control are getting closer to the transmitter, potentiallly moving objects that could attenuate or reflect Wi-Fi signals or set up a repeater to sit within range of both the base station and the location where you wish to have network coverage.