CRYPTARK

Vessels capable of dropping this will be labelled "-ARTIFACT-" and display "Keep Repair System" like the description says.

The trick to not destroying the Repair System is it can only rebuild the most recently destroyed system. Therefore when destroying something you really want to stay dead, quickly go take out another system afterwards such as Nuclear Defense or Door Systems. The Repair System will then switch to repairing that and the previous system will stay dead. The other option is equipping something like the Nuke Rocket, which takes out most lower level systems in one shot. Simply fire and fly to the next system to kill. Cheers!