Why does my sb600 stop working wirelessly after a few shots with my Nikon d40?

The connection works well for a while and all of a sudden my flash will stop responding. Are there settings I need to adjust? I know it can't be the batteries because they are fully charged.

There are a number of reasons for this but two come to mind.

1) The recycle time lengthens as your shooting rate increases. So if you are trying to use your camera in the "burst" mode, eventually the flash has to catch up.
2) Electronic flash units are NOT designed to flash repeatedly like the strobes at a concert or night club. At some point the flash tube gets too hot and the unit will protect itself and stop working until the bulb is back into its safe operating temperature range