In Contact, the major point of contention in the latter half is whether Eleanor had actually traveled to another planet or whether she was just hallucinating. Why couldn't they just try again with another person? Or a dozen more for that matter.
The machine had already been built and there is nothing in the movie which says that it could be used only once.
Given the expense ("Why build one when you can build two for twice the price?"), loss of life and controversy, only for the pod to seemingly just fall through, there wasn't enough political willpower to fund a second attempt -- the Congressional hearings led by Kitz was an attempt to scapegoat the immense failure on Hadden as an elaborate hoax.
Conceivably there is a number of people (scientists, technicians, etc.) who are aware of the 18-hour recording discrepancy, but surely there are many (Kitz probably among them) who would want to cover it up or pass it off publicly as a crack-pot conspiracy theory. Given that, and the government's unwillingness to proceed further, it's probable no private entity would be willing buy out and fund such a PR disaster either.
Finally, while there's also nothing in the movie that says it can only be used once, it also doesn't say it can be used more than once. It's possible the machine was designed for a single trip only. However, that wouldn't stop a third (or more) machine from being built. The plans didn't cease to exist, provided someone was willing to pony up an exorbitant amount of cash.
Keeping the book out of this, it seems to me that Ellie and her 'father' answer this during their discussion while Ellie was on her 18 hour trip.
Ellie: Do we get to come back?
"Dad": This was just a first step. In time, you'll take another.
Ellie: But other people need to see what I've seen...
"Dad": This is the way it's been done for billions of years. Small moves, Ellie. Small moves.
The above text suggests to me that even if the machine were to be tried, it wouldn't work anyway... given that the whole thing is regarded as a hoax by the 'establishment', AND Ellie's report would contain the information that it wouldn't work, I'd imagine no one in their right mind would consider the expense of trying again.
It is implied at the end of the movie that there are those questioning Kitz's reasoning... in the doubt shown by the president.
