Why does linear airfoil theory break down at hypersonic speeds?
The linear theory makes certain assumptions in its formulation:


The flow is irrotational and isentropic.
The perturbations are small; i.e. the bodies are small at small angles of attack.


However, hypersonic flow violates these assumptions:


For a body in hypersonic flow (blunt body with detached bow shock), an entropy gradient is developed that varies along the distance of the body. It results in an entropy layer that persists all along the body.
In a hypersonic flow, the viscous boundary layer interacts with the shock and entropy layer and the kinetic energy of the flow is dissipated by the effect of friction within the boundary layer. Due to these viscous effects, the flow is no longer irrotational.


Note that the linear theory is not applicable if the flow is considered hypersonic. M > 5 is usually taken as hypersonic. Linear theory is not applicable in transonic regime either.