The answer varies by species and by individual. Thamnophis sirtalis normally lives 8-9 years in captivity, but if I recall correctly has lived up to around 15 years? I think someone just posted that a T. ordinoides actually lived to be 17 years old? Can somebody help me out there? Anyway, I wouldn't count on yours reproducing beyond 7-8 years of age, but there are always exceptions. The very old ones might not reproduce a year or two before they die, but I suspect that most do just find until they die.

To show the species contrast, T. gigas normally only lives to be 4-6 years old, so it obviously wouldn't continue reproducing as long as other species.