http://en.wikipedia.org/wiki/Sassanid_Empire
That was the vacuum that Islam (then nascent) filled. Only after seizing the remnants of Persia (and, critically, control of the silk routes running through it) could the first Caliphate move into territory once controlled by Constantinople. By the time the second Caliphate had extended Islam's control into Spain, more than four centuries had passed since the abandonment of Rome as a capital city (330 CE), after which the city persevered for another century before being sacked entirely. However the Western Empire was long gone by the time Islam appeared in the territory it once controlled.
http://en.wikipedia.org/wiki/File:Map_of_expansion_of_Caliph...
In fact, the very word "Zealot" originally referred to a particular religio-political movement that sometimes dabbled in what we might in today's terms call "terrorism".
In some ways, the Western Empire was sort of doomed from the time of Augustus onward when their embedded fear of the German tribes was established[0]. The defeat at Teutoburg Forest and the loss of around 20,000 Roman legionaries stopped all expansion into Germany and most likely lead the the eventual confrontation with the Goths. There's also a "what if" due to the Huns and pushing the Goths across the Danube, but if it were not the Huns, it could have been other factors as well (famines or another barbarian tribe).
The Eastern Empire almost reconquered the Western half in the 6th century under Justinian[2] and Belisarius[3]. However, internal bickering and mistrust led to squandering much of the gains that were won.
The Islamic forces were also able to capitalize on the chaos brought on by the perpetual wars between the Eastern Empire and the Sassanids[4] as well as the various barbarian tribes (such as the Bulgars and the various Gothic tribes that filled the vacuum of the former Western Empire) that still preyed on the Constantinople and other areas. There was just too many fires to contain them all at once and when one was put out, another was started in another region.
Honestly, I think it was for the best the Roman Empire ended for the sake of renewal (as much as I love Roman History). It had started to stagnate by the forth century and the more Greek side in the Eastern Empire was far from being the intellectual and cultural epicenter that it was during Classical Greek times. Sure, they built great things such as the Hippodrome and the Hagia Sofia, but those were just reincarnations of similar things done under the unified empire.
[0] http://en.wikipedia.org/wiki/Battle_of_the_Teutoburg_Forest
[1] http://en.wikipedia.org/wiki/Fourth_Crusade
[2] http://en.wikipedia.org/wiki/Belisarius
If you thought the gcc/egcs fork was a big deal ...
Byzantines with a more Greek Culture (and spoken language) and different religious practices in some ways, despite being part of the same Catholic Church. I'd imagine that many in the West by the time of Justinian viewed them as invaders as much as any of the other groups.
Mistrust of foreign cultures still plagues us today in most countries throughout the world. It's too bad we do not learn from the mistakes of the past, such as those of the Romans and Gothic tribes. Isolating your fellow man because he speaks a different language or has a different culture/religion ends up making a country less safe instead of more safe.
[1] http://en.wikipedia.org/wiki/Gothic_War_(376-382)#Outbreak