The ultimate definition of 'stability' in football would have to be remaining in the same division year in, year out. Curiously the last two times we've managed 8 seasons at the same level were both in the 2nd tier (1973-1981 being the most recent). Nothing can better 8 other than the 16 season run in the top flight that ended in 1913.
Conclusion - top two tiers is where Notts find stability.