The rings only repair when you kill the last segment of the outer ring (see manual, page 4). Then the middle ring is moved to the outer ring, the inner ring to the middle ring and a new inner ring is created.
So keep at least one segment of the outer ring intact. Then you can create big holes in the inner and middle rings and kill the gun.
BTW: The arcade version is even harder. Especially the difficulty ramp up is very fast and the game becomes extremely hard very soon.
Edited by Thomas Jentzsch, Fri Aug 12, 2016 3:42 AM.