[NicknamedBob]

"...how long would a Space Frontier last if it were ever opened by establishing private property rights?"

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.

[RightWhale]

I think that is a fair estimate.