In many of the areas there were formerly Greek speaking populations. There was once a large community of Greek speakers in Anatolia, for instance, from the Byzantine Empire. Have a look at this and this

Part of it in my area of knowledge is that Greek just didn't have the penetration into general society to be the majority language long-term. In Judea, the elites spoke Greek in many cases, but the it never filtered down the social ladder. And eventually another language, Arabic, that spread prolifically in the Middle East, displaced the pockets of Greek that were left.