The declining quality probably correlated with the military setbacks the Byzantines were dealt by the Arabs and later by the Turks. Heraclius finally defeated the Sassanid Persians in 622 but lost much of the Holy Land to the Arabs by 640. [1,2] The crushing defeat of the Byzantines at Manzikert in 1071 [3] led to a series of events that resulted in the Crusades.

[1] https://en.wikipedia.org/wiki/Heraclius#Byzantine_counter-of... [2] https://en.wikipedia.org/wiki/Battle_of_the_Yarmuk [3] https://en.wikipedia.org/wiki/Battle_of_Manzikert