Monostable Multivibrator using Op Amp, from this link,
Obviously there is a certain amount of time that the capacitor takes to charge again from -Vcc*β to VD (0.7v) and therefore during this period a second negative pulse may not start a new timing period.
Wouldn't a negative pulse force the op-amp into negative saturation, since at any point the voltage would be less than VD(0.7), thus starting a new time period