Much is made of the Huns, Visigoths, ect who were always on Rome's northern boundary. These groups surely cost the Empire greatly. Two threats from the south proved in the end (along with the actions and subsequent consequences of those in the 4th Crusade), however, to cause the Fall of Constantinople. First, the Romans had just wrapped up a war with Persia, that was on- again and off-again for almost a thousand years. And this isn't just one group of Persians, it is a collective of all citizens of Persia from the Armenian and Kurdish regions to the Panj River and the Hindu Kush.
The second major power that threatened Rome from the south were the Muslims. This new force that emerged from the Arbian Peninsula during the Seventh Century had defeated Jews and other tribes on the Arabian Peninsula, totaling more than thirty battles in which they were victorious. Then, the Arab people had to deal with the various cultures in the Levant, which they did to establish the Umayyad Caliphate in Damascus. It is quite remarkable indeed that this force made it out of Arabia and conquered the Levant, and if it were to be "Gamed-Out", certainly the chances are less than forty precent that they emerge as victor. In addition, it is quite likely that had not the Persians been fighting with the Romans for 800 years, they would have defeated the Arabs in the Levant. The Arab Muslims fought and fought with the Persians to not only convert them from Zoroasterism to Islam, but also Arabize the Farsi, the Kurds, the Balochi's, ect. Islam spread slower in East Persia (Khorasan). But it spread nonetheless. By the middle of the 700s, Shi'as began siding with one popular fighter and descendant of Muhamad's uncle, Ali Ibn 'Abd Allah Ibn al-Abbas.
Photo: https://ferrebeekeeper.wordpress.com/2015/08/17/the-crown-of-shapur-ii/