Jefferson said in his inaugural that the West would last for thousands upon thousands of generations of honest, moral, and hard-working farmers. Ignoring that the West as a frontier barely lasted for four generations, how long would a Space Frontier last if it were ever opened by establishing private property rights?
Corporations get leases and private citizens get deeds.
Extrapolating from the given example, between four hundred and a thousand years.
Primary factors are:
Limited access
Limited expansion capacity of emigrant population
Tremendous area of expansion -- Mars has twice the dry land area of Earth, plus nearly a hundred moons that could be settled elsewhere.
If one accepts that the Oort Cloud has potential, it could last several thousand years, and would lead naturally to interstellar colonization.