  Recent observational missions have uncovered a significant number of compact
multi-exoplanet systems. The tight orbital spacing of these systems has led to
much effort being applied to the understanding of their stability; however, a
key limitation of the majority of these studies is the termination of
simulations as soon as the orbits of two planets cross. In this work we explore
the stability of compact, three-planet systems and continue our simulations all
the way to the first collision of planets to yield a better understanding of
the lifetime of these systems. We perform over $25,000$ integrations of a
Sun-like star orbited by three Earth-like secondaries for up to a billion
orbits to explore a wide parameter space of initial conditions in both the
co-planar and inclined cases, with a focus on the initial orbital spacing. We
calculate the probability of collision over time and determine the probability
of collision between specific pairs of planets. We find systems that persist
for over $10^8$ orbits after an orbital crossing and show how the
post-instability survival time of systems depends upon the initial orbital
separation, mutual inclination, planetary radius, and the closest encounter
experienced. Additionally, we examine the effects of very small changes in the
initial positions of the planets upon the time to collision and show the effect
that the choice of integrator can have upon simulation results. We generalise
our results throughout to show both the behaviour of systems with an inner
planet initially located at $1$ AU and $0.25$ AU.
