It was reopened in the 1200/1300 period by the Mongols at great expense in men and treasure ~
Where did you see that the Silk Road was shut down between 535 a.d. and reopened some 750 years later? I’ve never read that anywhere.
Silk was always in great demand in Europe, and Byzantine royalty highly valued it. Later, the Republic of Venizia took control of trade with nations to the east - it is how Venice became a powerful Republic.