The stability of short laser pulses propagating through plasma channels is investigated theoretically.Perturbation to the laser pulse are shown to modify the ponderomotive pressure, which distors the dielectric properties of the plasma channel. The channel perturbation then further distors the laser pulse. A set of coupled mode equation is derived and a matrix dispersion relation is obtained analytically for the special case of a quadratic radial density variation. As ana example, the spatiotemporal growth of the pure dipole perturbation is evaluated in various parameter regimes. Mechanisms for suppressing the instability is discussed.