Jason dies when while leaned against the rotting hulk of the Argo, the ship that he and the Argonauts took on their quest. This pathetic and bitterly ironic death seems to be totally symbolic of sorry state of the Jason's life. Let's pick it apart a bit...
First, there's the fact that the Argo is just sitting around and rotting. Here's the famous ship that took the famous Jason off on his famous voyage. Like Jason, the vessel is a legend in its own time, but now it sits neglected on a beach. Just like Jason, the boat is forgotten. Without another quest to go on, Jason and his ship are both falling apart.
Just when you thought you were safe, we add another layer. The fact that Jason is killed by a falling chunk of the rotting Argo is also pretty symbolic. You could see the Argo as a symbol for all that Jason achieved, since it's the ship that took him on his great quest. But now, a piece of that same ship that kills him. (This would be where the bitter irony comes in.)
Could it be that Jason's death-by-Argo symbolizes that it's Jason's quest that eventually brings him to a bad end? If he'd never gone on the quest, he never would've met Medea, and perhaps he never would've gotten such a big head that he thought he could kick her to the curb without any repercussions.
Also, it could be that the symbolism is even bigger than just Jason. What the story might be saying is that when any human being strives to do great things, he or she is risking failure. And beyond even that, they may just be planting the seeds of their own destruction.