I have always held a theory that, because the characters on the battlefield can survive things that would kill any person in this world (such as getting impaled with enough force to injure the person behind them or being burnt with a flame thrower), all characters on the battlefield with more than about 8 hp have a sort of shield around them on the battlefield. As the combatants receive injuries, damage is done to the shield, but not the actual combatant. When a combatant's hp falls to zero, their shield has been penetrated, and they receive a lethal blow. A healer would strengthen the shield around the combatant, thus allowing them to take more damage. This theory would mean a combatant could fall off the roof of a building and not break a leg (which Arman can do in one mission). This would also explain why you or your teammates' health increases with an increase in psy defense. Combatants do not need to grow physically stronger to survive more; they just need to increase their mental defensive abilities. So, if my theory were correct, shields do not "heal", but they do increase the strength of the preexisting shield around the combatant, which weakens as it receives damage but protects the combatant from lethal blows, thus preventing them from dying in a few sword strokes or spear jabs like ordinary people would.
I hope I was not too confusing.
I hope I was not too confusing.