Roberts (1969) first realised that stationary spiral shocks can arise in the interstellar medium of a disk galaxy as a response to an externally imposed spiral gravitational potential. This has broad consequences: for example these are thought to be important sites of star formation. But are these shocks stable? We find that boundary conditions are critical in determining whether the solutions are stable or not. Shocks are unstable if periodic boundary conditions are imposed. The instability disappears if boundary conditions are imposed such that the upstream flow is left unperturbed as in the classic analysis of D’yakov and Kontorovich. This reconciles apparently contradictory findings of previous authors. This also shows that the instability is distinct from the Kelvin-Helmholtz instability. We suggest that instability is a general characteristics of periodic shocks, regardless of the presence of shear, and provide a physical picture as to why this is the case.