I've played games with "body armor rules" before (Heartland comes to mind), wherein at special times during games, certain players were allowed to take one extra hit to centermass before calling themselves out. THis is generally how real body armor works, too, but it's entirely dependent on range, the exact type of projectile being used, angle of deflection, the exact composition of the body armor, what kind of plate you've got installed, whether or not the armor is wet, how old the armor is... Et-cetera.
That said, a real SAPI Level III armored vest won't stop a .223 round, and guess what most players are using?
Yep.
M16's.