A space-time discrete-adjoint method recently developed for high-fidelity compressible turbulence simulations is extended to chemically-reacting mixtures for the purpose of measuring sensitivity of localized ignition in a non-premixed hydrogen-air mixing layer. The ignition source is modeled as a source in the energy equation, which introduces several parameters that need to be chosen with care. Because ignition is inherently discontinuous in parameter space (i.e., it succeeds or fails after some period), the resulting gradients in modeling parameters are ill-defined near its threshold. To this end, a cost functional is designed to provide short-time sensitivity in concert with an indicator function that informs whether or not successful ignition has occurred. The corresponding sensitivity is used in a line-search algorithm to identify a point on the ignition boundary in high-dimensional parameter space (7 dimensional in our 7-parameter demonstration). This is used to quantify the relative importance of parameters on ignition.