The first part of the difficulty is “when” and the problem stems from the calendar itself. Did The Prophet die in January or June? We use a much different calendar system than Ancient Middle Eastern world, so it is difficult to say whether The Prophet died in June or January. Compounding the difficulty concerns the fact that days were often recorded and recalled in a different manner than we would. For example, a “springtime” day does not necessarily mean a day between what we know as March, April or May. Those of us who live in the South know first-hand that temperatures can reach the 70’s in the middle of December, a “springtime” day. Some holding to a June demise of Muhammed often refer to the day being a warm day, but this does not mean the day fell in warm months.
Sources disagree on other details the date of his death beyond. There is no agreement on exactly how he died, or where. Some say he died by poisoning while others say he simply passed after periods of extreme headaches and fatigue--and both claim source material. Some accounts tell of a few women who mourned his death by celebrating the freedoms Muhammad taught but they were punished for their observance by losing their hands to the sword.
If I understand correctly the implications are these: 1) death is not a celebratory event, especially concerning Muhammad; and 2) the writings and work of Muhammad are honored based on his life. The Prophet is considered to be a man among men, a gem among stones (as it were) and instead of being worshipped (Allah alone is to receive worship), Muhammad and his activity are symbols of Allah’s activity in the world.
A number of features become outstanding regarding the demise of The Prophet: first, there are no prophetic descriptions of his death from God. No one saw it coming. Muslims often comment that Muhammad became increasingly aware of the time of his death, but God makes no prophetic announcement.
Second, he remains dead. Karen Armstrong writes in her book, “Muhammad: A Biography of the Prophet” that refusal “to admit that Muhammad had died . . . was to deny the basic truth about Muhammad” (p. 257). Islam teaches that he is no more than a messenger and has died like other messengers before him.
The Prophets that came before Muhammad have died--Jesus included; however, consider that Jesus' birth, death, burial and resurrection were described by God through the Prophets long before He was born and all these came long before Muhammad. The circumstances of Jesus' death, burial and resurrection are recorded in the Injil (The Gospels) and cannot be changed.
Why do you doubt? Have you not read the Holy Books that came before?