[vijay_nair]

Punctuated equilibrium[1] — growth followed by sudden collapse — could be the umbrella term for the scenarios you are thinking of.

The phenomenon, originally from biology, shows up in sandpiles and avalanches as well; it could explain the growth (or lack of it) of mountains too.

[1] https://en.m.wikipedia.org/wiki/Punctuated_equilibrium

[TheSpiceIsLife]

For any particular mountain or mountain ranger there could be a number of processes, some of which may dominate for periods of time.

It could be slow / fast growth followed by slow / fast sinking / decay / collapse / asteroid impact / weathering.

I image there have been a number of sequences that have played out in various locations over time.