  Superconducting nanowire single-photon detectors are set apart from other
photon counting technologies above all else by their extremely high speed, with
few-ten-ps timing resolution, and recovery times $\tau_R\lesssim$10 ns after a
detection event. In this work, however, we identify in the conventional
electrical readout scheme a nonlinear interaction between the detector and its
readout which can make stable, high-efficiency operation impossible at count
rates even an order-of-magnitude less than $\tau_R^{-1}$. We present detailed
experimental confirmation of this, and a theoretical model which quantitatively
explains our observations. Finally, we describe an improved readout which
circumvents this problem, allowing these detectors to be operated stably at
high count rates, with a detection efficiency penalty determined purely by
their inductive reset time.
