According to the insider rumor mill Prince contracted AIDS back in the 90's but kept it under control with medication. Then his church (JW) convinced him that God had cured him and he should stop taking the medicine. The AIDS came back in full force. I don't vouch for this info, I'm just passing it on.
So often, when something makes sense, it’s true.
His final public appearance was 5 days before his death. If he was near death from AIDS, it would be very visible, and there would have been no public appearance.