OP, I can definitely feel your frustration although as others have mentioned, it's truly dependent on a lot of circumstances. Just last week on a flight home, the GA wanted to close 15-20 minutes early (flight was maybe ~20% full) and I could overhear the captain asking her how many connecting passengers we were waiting for. Sounded like there were at least 3-4 and captain said no dice, leave the door open. After 3 of them showed up and we were nearing ~5 minutes until scheduled departure, the captain let her close the door. Knowing there was another flight an hour later that was practically empty, I'd say that's fair.
As cfischer mentioned, I've had luck twice in the last year or so asking/begging the GA to call the other gate and let them know I was running and would be there in time.