This is not really an accurate statement. More accurate would be "a religion that has yet to sustain a democratic or prosperous society". While I agree that there are no true examples of a democratic muslim state, with perhaps the exception of Egypt, if one is willing to use a very liberal definition, there are prosperous arab societies.
The problem they have had in terms of prosperity is the unwillingness of the members of the society to continue to do the work that btought about the prosperity. If one looks at nations like Saudi Arabia, Kuwait and some of the smaller nations to the south of Saudi Arabia, we can see prosperity.
The problem comes when they start to import workers to perform the tasks that led to the prosperity. Soon these workers become a large lower class. The amount of work remains stable while the population of workers continues to increase.
As the society grows, the wealth becomes distributed among more members of the society. There is a propensity, however, to continue spending at the same rate as was previously possible. The end result is that spending outpaces income, and the wealth deteriorates.
There is also a notable absence of re-investment of wealth. The members of society with wealth are pleased with the status quo and tend to pass on opportunities to develop more or better industries which could increase their wealth. Again, this results in a failure to maintain prosperity.
The Saudi example shows very clearly how a society can become prosperous, and the fritter the wealth away like a sailor on shore leave in Thailand.
Fritter? Sailors don't fritter.
This is a good point. They are like trailer-trash lottery winners who whoop it up while the money is flowing in without ever producing anything worthwhile. The arab world isn't powerful because of any inherent worth. They just got lucky.