Generally I wait until STD if there are missing pax and in this age of web check-in that is quite frequent. If they have bags at the aircraft and I know that I can make up time enroute for an on time arrival and I know the aircraft isn't on a minimum time turnaround for the next sector and that the current and subsequent flights are not slot constrained I would give until +5 at the latest. Once the push request has been made that is game over for the late pax for two reasons - 1) there are too many other competing interests from the ramp space to runway position and the ground crew's next task and 2) it sets a poor precedent.
SR