In reply to foxtrapper:
I've heard it both ways too. Some state DNR and hunting sites recommend against the prolonged chase for that reason.
This from a venison preparation site:
Panicked deer flood their body with adrenaline when they’re in danger. Their heart races and blood pours into their muscles. The extra blood helps rev up the muscles for flight, but produces lactic and pyruvic acids in return. These acids, extra blood, and adrenaline are the major reasons venison tastes wild or gamey.
Maybe the motive against the prolonged chase is to get hunters to wait and take one good heart/ lung shot (or pass) instead of emptying the entire berkeleying magazine on one deer.