Would the second time you were scared half to death only act on the half remaining from the first scared half to death experience? The result being only a quater alive. If this is the case you would die exponentially and even an infinte number of scared half to death experiences will not result in total death.
Provided one was fully recovered from their first experience of being scared half to death, then I can see no reason why a subsequent half-scaring to death would result in physical harm any greater than the first experience. If, on the other hand, one has some pre-existing condition that makes them particularly vulnerable to the effects of a half-scare, then such half-scare could see one shuffle off this mortal coil.
What if a cat, having already lost 1 of its nine lives, was scared to half to death by another cat. Would it then have only 7.5 lives, or would it have four lives?