An initially stable 85Rb Bose-Einstein condensate (BEC) was subjected to a carefully controlled magnetic field pulse in the vicinity of a Feshbach resonance. This pulse probed the strongly interacting regime for the condensate, with calculated values for the diluteness parameter (na^3) ranging from 0.007 to 0.3. The field pulse was observed to cause loss of atoms from the condensate on remarkably short time scales (>=10 microseconds). The dependence of this loss on magnetic field pulse shape and amplitude was measured. For triangular pulses shorter than 1 ms, decreasing the pulse length actually increased the loss, until extremely short time scales (a few tens of microseconds) were reached. Such time scales and dependencies are very different from those expected in traditional condensate inelastic loss processes, suggesting the presence of new microscopic BEC physics.