One problem related to headlights turn off while driving has been reported for the 2004 GMC Envoy. The most recently reported issues are listed below.
Ac plug to fan motor burnt/melt, daylight/headlight connectors melted multiple times had them replaced 3 times each side. . . Cluster/ radio/ac lights burning out lights out on different areas from illumination to gages to radio and ac control button lights head lights went out while driving so did cluster, radio and ac lights had the cluster replaced by dealer while under warranty back in 2013 over cluster shortening, had my radio replaced as well by dealer same time.