I'm really intrigued by Indy Johan's idea of Indy dying by his whip finally fraying on a particular swing. I think that would be a very haunting, but very apt Indy death. Also, of course, the irony would be it's previously saved his life more than his gun and fists have...
I philosophized a bit about Indy's dead and here here is my version (fits to the facts we get from the Young Indy serial):
Indy is not dying in an adventure because he still lives as an old man telling stories to his grand children. That's a fact.
Indy has been searching all his live: for artifacts, for knowledge, for fortune and glory. But I think that's not what he's really looking for - he is on a quest for something higher (sense of life maybe). He probably isn't aware of this, he just feels the need to search. And in his old days he finally understands that, maybe finds his personal sense of life and dies in bed with finally having found peace and answers (the greatest finding/ disovery of his life).
My theory to the grail is: he got some extra power/ health/ years from drinking from the holy grail, to get immortality you would have to drink from the grail regularly.