One reason cited by historians is the decline of Byzantium’s control of land trade routes and peripheral territories. This allowed the sea traders on the Arabian Peninsula to exert more and more control over trade and to accumulate wealth until they could afford to finance conquering armies to capture the Middle East and North Africa.
Don’t buy it.
Merchants that become more successful do not generally morph into conquering armies. At least I can’t think of any examples. They expand their merchant activities, instead. Merchants are more likely to turn warlike when their trading activities are blocked.
IMO the Roman and Persian Empires had fought each other into a comprehensive state of utter exhaustion, something like some claim would have happened had we stayed out of WWII and allowed the Nazis and Soviets to destroy each other. (I’m not one of these people.)
So I think there is no question there was a major power vacuum in the Middle East. The question is why the Arabs, who had absolutely no tradition of conquest, suddenly became conquerors for a century. And then stopped again.
Again, IMO, the answer is the power of a new religious idea that fitted exactly into the pre-existing ideas of the Arabs.
Another explanation I’ve heard is that the sea routes were working more effectively and this impoverished the caravaneers.
Mo worked the camel caravans. When pirates or predatory governments made movement of goods via the Red Sea or Persian Gulf too expensive, merchants switched to camel caravans across the Arabian Peninsula, which were of course much more expensive than water shipment otherwise. This was the major economic activity of Arabia, supporting most of the townspeople like Mohammed’s clan. Even the Bedouin depended on the caravans. No caravans, raiding isn’t very profitable.
Supposedly an economic crisis in the peninsula preceded the Muslim explosion, possibly caused by switch to water rather than land shipment.
Here’s the real reason for the Arab “explosion” out of the peninsula: the tribes along the Levant were nominally Christian - Monophysites: http://en.wikipedia.org/wiki/Monophysitism - the Ghassanids: http://en.wikipedia.org/wiki/Ghassanids guarded the trade routes. Eventually, the Byzantines attacked the leadership as heretical and Islam was welcoming. Once they became oppressed by Byzantium they decided to switch and depredate the trade routes themselves. Hence Islam, the religion of predation, was a perfect match.
You’ll note that once other people’s money runs out Islam slows down quite a bit.
I think you're focusing on West of today's Saudi Arabia, rather than East.
In relation to Mohamad & his followers, take a look at the section entitled "Raids on Caravans - Caravans & Trade as a Source of Wealth” in this page