The birth of Muhammad's empire also coincided with the deaths of huge numbers of infidels. Never underestimate the power of unrestrained violence in building and holding an empire together. And then there's the danger of a single Muslim empire controlling the majority of the planet's oil.
But Muhammed’s empire originally succeeded because the Arab tribes were too busy fighting each other to stop him. Later, it fell apart because they were too busy fighting each other. Arabs believe they have dual ancestry. Those of Yemen consider themselves superior to the Qys or Northern Arabs, because their earliest ancestor is believed to be a son of Eber. Those of Qys are mere descendants of Ishmael. The two groups will not intermarry. As Islam spread, so did this duality claim. Even in Mideival Spain, Northern and Southern “Arabs” were constantly feuding.