I'd guess the time frame on this one to be 1960's or 70's. Might be a bit earlier, but I do not think it later than the late 70s.
The story is set on Earth, and centers around a soldier who has been killed several times in a war that has dragged on for years between rival powers. The soldier is American (IIRC), and the enemy is probably one of the communist powers of that era. The war has gone on so long, and been so bloody, that there simply weren't enough fresh recruits to replace losses. As such, medical research developed a way to restore recently killed people to life. They can restore almost anything, except traumatic damage to the brain (i.e. a head shot).
The protagonist reminisces about being brought back and waking up on the operating table after being restored. He notes that the nature of needing to get people back into the fight as quickly as possible has meant certain short cuts in the operating room. One of his arms is a little longer than the other after being re-attached. His ears don't quite line up, etc. He longs to get that final death, as he is very tired of fighting. Unfortunately for him, the military requires you die a certain number of times before you get to RIP. It's similar to the requirement in past wars that you fly a certain number of missions before you can go home, etc.
The soldier is killed at least twice in the story, IIRC. The first time he wakes up, he thought he had met his quota. He then finds out that the demands of the war have led to retroactively increase the number of times you have to fall in battle before being allowed to finally die. At one point, the protagonist contemplates throwing himself on the poisoned barbed wire surrounding the base he's on, but realizes they'll just bring him back again.
The final death comes when the protagonist is shot in the head during a battle. An explosive-tipped bullet, IIRC. His last thought was that he finally gets to die. To his great surprise, he wakes up on the operating table again. The protagonist exclaims something along the lines of "but I took one to the head!" He described the surgeon's faces crinkling up as they smiled, or perhaps smirked, behind their surgical masks. It's explained a new technique has been developed that can "unscramble" traumatic head injuries, and that a head shot is no longer a permanent death.
The story closes with the protagonist going back to his duties, weary and thinking about the time when he'll finally get to die for good.