I am happy to tell you that you made an incorrect assumption regarding Charlie dying of natural causes. You see, like the most famous resident of London's Baker Street, Charlie Chan is eternal. He lives on.
While it may be true that his last public appearance was many years ago, there are Hawaiians who will tell you in very hushed and secretive tones that, on very rare occasions, a wizened and somewhat frail Oriental gentleman can be seen wondering the grounds around the little house on Punchbowl Hill. Almost mythic in appearance, and seen very fleetingly, this figure is often surrounded and aided by multiple members of what is presumably the latest generation of the Chan family.
Hawaiians are very respectful of the Chan family's wishes to protect the privacy of their most famous resident. Tourists and other outsiders who ask the locals where to find Mr. Chan are deliberately kept in the dark on this matter.
Fortunately for the rest of us we are able to relive his past exploits on film and in books.
Respectfully, you are mistaken. Charlie survived the struggle at the Reichenbach Falls with his arch foe Doctor Loveless and after a period of wandering through the American West he returned in "The Adventure of the Empty House on Punchbowl Hill" as chronicled by his biographer Bess Marvin. P.S. I like the eternal figure explaination best.