Revealing mistake: Whenever James, Sanborn, and Eldridge are riding in the Humvee, you can see panels of wood in between the doors and windows of the Humvee. If you look closely, the grain in the wood is visible.
Revealing mistake: In the explosion of the opening scene it is apparent that cut scenes have been shot with several hours time difference because the sun has moved. This is best visible in the reflection of sun in the helmet and shadows of the vehicles in the background.
Answer: The problem for the sniper was once he'd taken his shot, he was now pretty exposed. He didn't have a lot of cover and it wouldn't have taken the Americans long to figure out where the shot came from, hence why the enemy snipers made no attempt to move.
GalahadFairlight