This in not the "ultimate answer" since it may not fit everyone, but it may help some of you. A possibility is renting a car in the city of departure and leaving it in Eindhoven Airport. It's possible to leave it at any hour. You can drop the keys in a special box inside the airport (Go straight to the airport after leaving the car. Don't leave the keys in the mailbox near the renting agencies. The drop-off point for the keys is inside the main hall of the airport)
It may seem expensive for some intially but it will probably be cheaper than sleeping over in Eindhoven and it may be approximately as expensive as the train trip (depending on how many people are travelling).
It's worth checking!
Note: the nearest gas pump (that I know of) to the airport is around 6Km away. Don't forget to fill the tank before arriving to the airport or you may have to go back.