How does this research suggest the market is unstable? According to these authors, the market was (in their view) dangerously perturbed 18,520 times, more than once per day. In spite of that, it remained stable. The flash crash took an afternoon to recover from. Knight took a day.

If you perturb a system over and over and each time it quickly swings back to equilibrium, that's pretty strong evidence it is stable.