Insect-scale flapping robots are challenging to stabilize due to their fast dynamics, unmodeled parameter variations, and the periodic nature of their control input. Effective controller designs must tolerate wing asymmetries that occur due to manufacturing errors and react quickly to stabilize the fast unstable modes of the system. Additionally, they should have minimal power requirements to fit within the tightly constrained power budget associated with insect-scale flying robots. Adaptive control methods are capable of learning online to account for uncertain physical parameters and other model uncertainties, and can thus improve system performance over time. In this work, a spiking neural network is used to stabilize hovering of an insect-scale robot in the presence of unknown parameter variations. The controller is shown to adapt rapidly during a simulated flight test and requires a total of only 800 neurons, allowing it to be implemented with minimal power requirements.