Much concern has been shared on the forums over the non-shadow priests lack of survivability in Player versus Player combat. A non-shadow priest can win against spell casters in long drawn out battles because heals are more efficient that damage spells, it simply takes a considerable amount of time. Against rogues, a non shadow priest also has a chance to win, simply through DOT spells, fear, and spamming flash heal. Non shadow priests have very little chance against hunters and warriors, and are much better off running for help.

Luckily, priests are very hard to kill while they still have mana. Between renew, shield, dispel magic, and fear, a priest can stay alive while running for a long time.

In battlegrounds, priests are best off running around with a full group of five and staying near the back of the crowd.  As I mentioned earlier, many smart rogues will hang back with the priest, waiting for someone to sneak up on the priest. Healing spells have forty yard ranges and it is essential for the priest to use it!
 

As long as the priest is not separated from their party and their party is attentive, they should be fine. It is in the parties best interest to be attentive to the priest, because the priest is the one keeping them alive.