Sure he won't go down immediately, but they shot him in the back leg nowhere near the heart/lungs etc. that's a lousy shot no matter what.

Then they decided to eat dinner and make camp for the night before even starting to go after him.

They finally killed him with a gun anyway, just follow him immediately. He would tire out quicker if was actively being trailed, he wouldn't have been able to stop and rest so much as he did.