For the same reasons Rome couldn't conquer and hold the middle east, the empires of the middle east probably couldn't conquer and hold central and western Europe.
In addition to the strain on bureaucracy and administration, the simple fact is that all these empires are based on certain ruling economic and military principles. For the Romans it was heavy infantry. For the Middle East it was always cavalry, especially light cavalry. Once you get too far into the other guys territory everything is in there advantage.
Which is why most of the conflict regions have always been in and around the Mediterranean. The logistical and economic advantages of controlling the Med would allow someone to project force into the other guys backyard, but once you get too far from the sea your back to the problem of having an army and culture not built for the place your invading.
Sure, but in the same way that the regions of Europe that became Christian are in no way limited by the places controlled by the Romans, the same could occur with Islam; religious proselytization could extend Islamic influence far beyond the borders of the early caliphates. In 600 AD, Christianity still hasn't cemented itself beyond the Rhine-Danube frontier, and by 800 it's only extended to the Elbe. Even if Islam can't cement itself in the Frankish kingdom(s) and the British Isles, conversion by the Russians and Khazars plus stagnating/eroding Frankish and Byzantine Empires could mean that it's Islam that catches on in pagan Eastern and Northern Europe. Over a period of centuries, Italy could eventually land in the hands of Islamic rulers, potentially leaving only the lands north of the Alps and the Pyrenees and west of the Elbe with a solid Christian majority.