  We extend the existing quasiclassical theory for the superconducting
proximity effect in a chaotic quantum dot, to include a time-reversal-symmetry
breaking magnetic field. Random-matrix theory (RMT) breaks down once the
Ehrenfest time $\tau_E$ becomes longer than the mean time $\tau_D$ between
Andreev reflections. As a consequence, the critical field at which the
excitation gap closes drops below the RMT prediction as $\tau_E/\tau_D$ is
increased. Our quasiclassical results are supported by comparison with a fully
quantum mechanical simulation of a stroboscopic model (the Andreev kicked
rotator).
