I agree with Dorothy. These birds, like all other birds, depend on your feeding them once you start. I leave my feeders up too for about the same time, just in case there are any stragglers.
I do not think feeding them makes them stay longer. I can usually tell by the change in the afternoon light that it is getting time for them to leave. Plus they eat a lot more for about two weeks before they are going to migrate. They have this internal clock that tells them it is time to go so I don't worry. They have never failed to leave when the time is right.