You might have to fiddle with the settings. The exiting passengers need to leave the station completely (d.h. get past the exit gate) before the next set of passengers can get onto the car. If the car leaves before they have time to do that, you might have the setting “don’t block station” on. This will force the car to leave the station immediately after the passengers got off, if there are other cars waiting at the station. And/or you might have to set the minimum time at the station longer.
If entrance and exit gates are a bit apart from each other, the cars need to stop at the station longer than if they are directly next to each other. Because of that, different stations might need different settings, or, if you want to use the same settings everywhere, the cars need to stop longer than actually necessary at some stations to allow the passengers enough time at the other(s).
I can give you my current monorail settings later today, which seem to be working as they should.