It was abolished by the Emperor Constantine and so fell out of use in both the Eastern and Western Roman world - I believe this is contemporaneous with Constantine's baptism in 337 and done out of respect for Jesus. The practice was resumed by the Umayyad caliphate (see Sean A. Anthony's Crucifixion and Death As Spectacle) as a form of legitimizing their rule, essentially establishing themselves as peers of the Roman, Byzantine, and Sassanid emperors.