The circumstances of Arathorn's death are mysterious. In the later Third Age, it was unusual for even a Dúnadan of noble descent to live past 160, and lacking other evidence we might assume that Arathorn simply died of old age (as indeed the original drafts of Appendix A to The Lord of the Rings seem to suggest). The published version, however, marks Arathorn as dying a premature death, without remarking on the event itself.
Conceivably, he was slain by Orcs, which had begun to increase in numbers during his father's Chieftainship, while Arathorn was still a young man. The War of the Dwarves and Orcs took place during the early part of Arathorn's own rule, leading to the decisive Battle of Nanduhirion (fought in Arathorn's fifteenth year as Chieftain). After the Orcs' defeat in that battle, we know that bands of refugees fled into the south, and were later responsible for the death of King Walda of Rohan. Perhaps a stray band also escaped into the Northlands, eventually to slay the Chieftain of the Dúnedain in his old age. This is, of course, sheer speculation, though it does fit the known historical events of the time.