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 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.