Quote from Waross: There may be a finite time required for the signal pulses to stabilize in the internal circuits.
This is very much the case I was referring to. Even when rise times are not a factor, as the pulse width reduces to less than or equal to the tpd of the device, the output pulse starts to become shortened in width compared to the input pulse until ultimately the device will stop switching reliably. The propagation delay tpd is realiable only for input pulses much greater than tpd. It's not unreasonable that a minimum amount of pulse energy is needed to 'fire up' the device stages and propagate the full pulse width through to the output.