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Planetary systems with more than two bodies will experience orbital crossingsat a time related to the initial orbital separations of the planets. After acrossing, the system enters a period of chaotic evolution ending in thereshaping of the system's architecture via planetary collisions or ejections.We carry out N-body integrations on a large number of systems withequally-spaced planets (in units of the Hill radius) to determine thedistribution of instability times for a given planet separation. We investigateboth the time to the initiation of instability through a close encounter andthe time to a planet-planet collision. We find that a significant portion ofsystems with non-zero mutual inclinations survive after a close encounter anddo not promptly experience a planet-planet collision. Systems with significantinclinations can continue to evolve for over 1,000 times longer than theencounter time. The fraction of long lived systems is dependent on the absolutesystem scale and the initial inclination of the planets. These results haveimplications to the assumed stability of observed planetary systems.

Survival of non-coplanar, closely-packed planetary systems after a close encounter