The Western or Eastern? The Western half fell from a combination of corruption, their condescending veiws of surrounding tribes, and the widespread use of non-Roman soldiers throughout the legions. The Eastern half fell from its main source of conscripts and possibly revenue as well being overran by the Ottomans in Asia Minor, and its capital being sacked by formerly friendly crusading forces who had stopped there on their way to an attempted retaking of Jerusalem. This latter incident the never were able to fully recover from before the Ottomans finished the task of overruning Constantinople after a lengthy siege.