From what I've read in Wikipedia, John von Neumann made a stupendous number of contributions to economics, computer science and mathematics. Why, then, didn't he receive a top award in any of these disciplines?
I don't know about the Fields medal, but he could not have won the Nobel prize since the only appropriate one would have been the one in Economics, which was awarded for the first time in 1969, 12 years after his death. And the Turing award was awarded for the first time in 1966, 9 years after his death.
At the inception of the Fields medal it was intended to encourage young mathematicians, hence the age restriction. Nash was famously overlooked for the Fields medal because it was thought that ''he didn't need encouragement'' and was already on his way.
Also why did Poincare not win a Nobel Prize in Physics despite being nominated many times? One reason is the sheer breadth and variety of his achievements which made it very hard to zoom in on one particular achievement that could be used as the basis of being awarded the prize, probably a similar phenomenon happened with von Neumann as the range of his achievements was too much for anyone to even keep up with.
Polymaths typically don't win the prizes you might expect as no-one can keep up with their work, let alone single out a few things that can be made into a case for an award.