That's a bit of an assumption there. Start with the premise, have some else provide the meat, and finish with the conclusion. Beautiful, it avoids actually proving anything while still making an authoritative sounding claim.
In truth the Byzantine economy, that one main determinant of the capability of the state, was booming well into the 12th century. There was a short fiscal crisis in the middle-late 11th century because of the political turmoil, but not something life-threatening to the economy as a whole. In fact, 12th century Byzantium underwent a commercial revolution of a sort, in ways booming in capital production like the Italian city-states would do for another few centuries.
The economy limped on for another few decades after the 4th Crusade, finally all coming crashing down into terminal decline around the end of the 13th century. It's not too entirely unfeasible to say, however, that the situation couldn't even have been saved then, had the Byzantines been able to reacquire certain of their former lands. Silk and glass continued to be produced right through the third quarter of the century in some Latin occupied lands.