Pressure has an effect too, but it's counted more as stress cycles (shutdown > TO > shutdown), and termed LCF or Low Cycle Fatigue. Pressure vessels like casings are certified for a safe life, after which they are scrapped.
I not aware of pressure vessels being certified for safe life under a regulation. Quite a few combustion chambers blew up after numerous weld repairs beyond 50,000 cycles.
Of course it helps if the user volunteers to scraps them as often as he does rotor disks.