The thing is, there barely was. First off, something to point out is that Egypt was Roman, recently relieved from a Persian occupation, and not a separate entity. Persia and the ERE just finished a massive, 30 year long, existence threatening war, in which Persia occupied more than half the Roman empire only to be seemingly miraculously pushed back by the efforts of Heraclius, only a few years before the Arab conquests. While I can't speak much for the Persians, the Roman army was small, exhausted, and was still in the process of properly reestablishing itself in Egypt and the Levant. The battle of Yarmouk Destroyed what little was left of the Roman army in the area, letting the Arabs occupy the Levant without significant bloodshed. It was only through the immense efforts of the Emperors Heraclius, Constans II, Constantine IV, and later Leo III, that Roman possessions in Anatolia and Italy were secured from further Arab conquest.

In short, the Arabs were able to conquer the Western middle east because there wasn't a strong Roman military presence, not in spite of it. That's not to say that they didn't achieve impressive military victories, such as Yarmouk, but Roman power in the Levant was much more fragile than it had been.