A coronagraph on the Astrophysics Focused Telescope Asset (AFTA) provides a unique opportunity to conduct space based spectroscopic characterization of faint planets orbiting nearby stars. The principal components of such an instrument are the coronagraph itself, the integral field spectrograph (IFS) imager, and a wavefront control system to remove observatory instabilities and quasi-static speckles. Such a system will need to reach contrast levels between 1×10-8 and 1×10-9 at small angular separations to detect cool Jupiters and characterize exo-zodiacal light for any future flagship class missions. Here we define the two principal focal plane control laws commonly used in high contrast imaging, and perform a sensitivity study of the focal plane wavefront controllers to time varying low-order aberrations. The shortest possible timescale of these requirements is based on the time required for a Kalman filter estimator to measure the field. The integration time required to achieve adequate signal-to-noise in the estimation step is derived from the observing conditions, and the brightness of the target and its associated exo-zodiacal light. Based on this analysis we define tip-tilt and defocus stability limits, which must appear in the error budget for any low-order wavefront sensor intended for the instrument.