let take the AA example in the OP, could use the following in the AA's Init line.
this addEventHandler ["killed", {DEADBEEF synchronizeObjectsAdd [player];}]
Where DEADBEEF is the support requester and player is the unit you want to have support available to it.
I had forgotten some details as to how the support system works. Sufficient to say un syncing the player from the requester isn't enough because some of the support scripts are running on the player.
What you can do instead is try simply deleting the support provider via a script. This does have one potential issue if you end up deleting it while another script is using it you may crash.
this addEventHandler ["killed", {deleteVehicle ART1;}]
Where ART1 is the support module you no longer want provided.
One final caveat if this is going to be used for a multilayer map there is a seperate event handler and it's standard practice to have these handlers run scripts instead of directly placing code inside them.
Do things like this:
this addMPEventHandler ["killed", {_this execVM "myscript.sqf";}]
Avoid things like this:
this addMPEventHandler ["killed", {deleteVehicle ART1;}]