Stability is not a problem in the air while shooting at the planes, but it definitely is while shooting to the ground. Having available space is the key.
The game over dialog doesn't appear, but this could be because I'm running it in wine. Also, it's possible for planes to crash, it's kind of tricky, which makes even weirder the sudden crash of all the planes simultaneously. I'm adding a video to show you.
Since is a proof of concept I'm not sure what else to say since you don't mention a particular goal, so I'll tell you the options that I would consider for stabilization.
1. Leave it like that: use only planes, add quantity and variety.
2. Improve it: look for a mathematical model for planes.