If your on a Disney tour, Disney is responsible to get you to the next port to met up with the vessel. That means the ship will wait as long as it can or they will fly you on to the next port.
If you on a self booked tour, the vessel will likely also wait for you as long as they can, however if they sail it is your responsibility to catch up with the vessel.
The reasons the vessel may have to sail include costs to stay as the dock and a sailing time to arrive at the next port on time.
There are some video clips on bing and utube showing passingers trying to get to the vessel. They are indeed funny , sad and scary all at the same.time.
I have read the most common reason for passingers being late returning to the vessel is drinking.
AKK