The discussion below has all been very interesting, but there's a very simple explanation why there is no word for a parent whose child has died: there was no need for it in the law.

A widow or widower has a legal standing vis-a-vis the estate of the deceased spouse. Similarly, an orphan has a legal standing with respect to his parents' estate. The special legal circumstance for an orphan includes the state's taking on the responsibility for ensuring the welfare of the child. There was no need for such a word for one whose child or children died, since such an event did not provide or require a special status in the eyes of the law.


TEd