Update: I think I found the source of my problem.
Situation: I launch a rocket consisting largely of boosters. The rocket tips to the side and breaks apart.
Main difference: I wasn't using the Unity-style GUI. The window disappeared, but only for a very short moment. This leads me to believe my problem was caused by a bug in Unity or the Unity GUI. However, this was only after one try so I'm going to need to look into this more.