Don't give up on the idea of a certain player killing him - there are many walkarounds. I'd suggest using a single unit to kill him, a melee one. Tell the player that this unit must kill him of you lose. If your unit is right next to the enemy, deactivate a trigger making you lose if he dies. If he dies otherwise, you are defeated. The trigger will of course have to be turned back on and looping for when your unit is not next to him. There's always a possibility a CPU player could kill him, but it doesn't matter that much if you are attacking him at the same time.
You can also do something with the kills attribute if you can get the situation under control enough, to detect that another player didn't kill him. To prevent things from going wrong, you need to have as much control over everything as possible. This could mean using a separate player for the leader, and making only sure all CPUs are allied to it.
Immobile units AI doesn't stop a unit from moving at all, it just doesn't task it to explore/attack etc. The unit will still retaliate if you try to kill it, and you can still freely move it around with triggers.
Also, at the top, a trigger doesn't need to be turned off if it is not looping, and it has fired. The only way to have it fire again would be to turn it back on again, and turning it off can't prevent it coming back on from another trigger.
[This message has been edited by rwilde (edited 01-13-2006 @ 02:57 PM).]