This is one reason that I keep my hummingbird feeders up. It is not true that the hummingbirds will not migrate if you leave your feeders up until after Labor Day. In fact, I would say that it helps them on their southward migration, but this is only my opinion. As one can see from the photos below, the Ruby-throated is fattening up for the coming migration. Hummers also eat insects and spiders etc., so the feeders aren't their only source of food.
Another reason that I leave my hummingbird feeders up all fall (I leave mine up till Christmas here!), is that I hope for a western vagrant hummingbird species. Every fall, some Selasphorus (Like Rufous and Allen's) hummingbird species move east of the Mississippi River and show up at feeders in the Midwest and East. Other western species have shown up as well.
Here are some sites with more info:
Add your fall feeders to this map (Ohio only I think)!: Fall Vagrant Hummingbirds Project