That is the real start of the decline of Islam - they lived for centuries off being the middle men in trade between the east and the west.
The Byzantines were able to deal with trade direct to China for a time via their Jewish allies, the Khazars - and in a famous episode of Byzantine craftiness the Byzantines smuggled silk worms out of China making them the sole source outside of China for the stuff.
Islam declined the way it did because the Europeans bypassed them and they could no longer tax the trade between the east and west. The Muslims never recovered from their victory.
This is my opinion only and it is sort of worth pondering that for the Muslim world, capturing Constantinople probably destroyed Islam in the long run.
Really good observation. It is also noteworthy that after 1453 Western Europe started serious efforts to discover other routes to China and India. The resulting discoveries brought immense wealth into the west and it was from that point that Europe began to outstrip the rest of the world in power and influence. It is only since the advent of oil as a major source of wealth that (some of) the Islamic nations have emerged as influential in world politics.