It seems to me that it is a basic survival adaptation. When resources are scarce (no food), you can't support offspring. If you can't support offspring, your species doesn't survive. It would make sense that evolutionary branches where aging processes slow down during a time of scarcity would have an adaptive advantage. They live to breed another day.
Surely individuals who age slowly all the time would have an evolutionary advantage over those who only age slowly in times of starvation? The longer you live the more offspring you can have.
This leads me to suspect that our bodies can't just turn off the aging process.