Usually many if not most athletes can take it many more years from their late 30s. But what happens after 10 to 15 years of play is they lose their fire in their bellies and the game is not as fun to them so they move on. They still have the skills for a decade or more, but lose the drive.
Manning is still very hungry.
Torii Hunter is also nearing 40 and still playing some fine baseball.
I think A-Rod has a fire BELOW his belly and needs to play to pay for expenses.