I receive this question quite a bit. The answer is "it depends".
Let's first back up and answer a related question: Will my hummingbird feeder prevent the hummers from migrating for the winter? The answer to this is an unequivocal "no". The timing of fall migration is physiologically triggered by decreasing day lengths. Furthermore, these physiological changes are genetically based. As such, there is always variation in the population with some hummingbirds genetically getting the urge to migrate sooner, while others get the urge only later. Statistically, this variation will show up as a bell curve with some average date for migration departure, and most hummingbirds will depart near this average date. For Northwest Arkansas, this is around the middle of September.
Complicating things a bit is the migration from the north. As birds leave the north for the southern areas, a back-up starts to occur. Our birds haven't quite left yet as the northern birds start to arrive. This actually creates a spike in hummingbird sightings during September; more than any other time of the year for NWA (see eBird.org Ruby-throated Hummingbird chart).
So, back to our original question of how long will hummers be at your feeders this fall...I said "it depends", because it pretty much depends on how many hummingbirds you tended to see during the summer. These are your resident birds. Any individual transient from the north will only be around a few days as it passes through, even though it may take a couple of weeks for the entire population to do so. But they are already migrating, so pass on through they will. The genetics of your resident birds will determine the likelihood that you will have hummingbirds into October and later.
If you had handful of hummingbirds regularly at your feeders this summer, then the odds are that all of your hummers will be gone by the end of September. If you had scads of hummingbirds in your yard (100+), then the odds are more in your favor that at least one of them is genetically a late season migrant. He/she may be around until later in October or possibly even into November.
So, keeping your hummingbird feeders up into the late fall will not prevent the birds from leaving for Mexico and Central America. However, it will help those few late season migrants to survive a little better, and fatten up a little more, for when it is their turn to head south.