The sensitivity of the radiofrequency (rf) wave generated by the free electron laser portion of a two-beam accelerator (TBA) is analyzed, both analytically and numerically in a "resonant particle" approximation. It is shown that the phase of the rf wave is strongly dependent upon errors in the wiggler strength and wavelength and upon the electron beam characteristics of energy and current. The resulting phase error is shown to be unacceptable for a TBA, given reasonable errors in various components. A feedback system is proposed which will keep the rf wave phase within acceptable bounds. However, the feedback system is, at best, cumbersome and a simpler system would be desirable.