I view it as your at a point were you have been weakened that you are completely stunned and unable to continue using mana in your duel without assistance from someone else. The duels are more of duels of the mind brought out into the physical plane.
You are defeated, but not dead. Just as in Player vs Environment, if your team mate gets defeated they can be revived to help continue the fight against monsters. The same goes for Player vs Player. As long as you don't flee you can be revived. It is valuable to have a team member who has spent training points in the Life School or even better to have a primary Life student who can use power pips toward healing spells and use spells that heal everyone on the team.
This may lead to some more complicated strategy decisions. Who is the healer on the team? You may want to try to target them first. And if you have a healer, you may want to try to protect them. Who knows, maybe we'll have Life students dying their clothes to be less identifiable and Ice students dying green!
personally i find it unfair in pvp that a death student has the sacrifice spell AND the pixie healing spell. that means that they can heal 8 times! (based on my deck, i have 4 copies) i find this extremly unfair because death students can already steal health with buffed up ghoul and vampire. i think that if a death student dies from the sacrifice spell, they SHOULD NOT be healed. this is fair because you can actually RESIST the sacrifice spell with good enough clothing.
and by the way, their not dead, they're defeated. as long as they don't flee their partner can heal them