We don't have anything like exact percentages for literacy in the pre-modern era, let alone on a century-by-century basis. Moreover, the "Middle East" is a pretty big place and there would have been incredible regional variation as well Urban/Rural variation.

That being said, Marshall Hodgson's points on this are quite good, writing in his second volume of the The Venture of Islam, covering the 10th to the 16th century:

Education was very widespread, by the norms of agrarianate times. Almost any gifted boy would know something of the meaning of reading and writing and have the opportunity, at the Qur'an schools which were found even in villages, to master the rudiments that would then allow him to pursue his studies further, supported by a waqf endowment.

On the most elementary level education means literacy. But the usefulness of universal literacy can be exaggerated. Figures giving the percentage of literates in a population do not indicate dependably the proportion of the population that can be reached by written means. The use of letters can be quite widely fonnative of the social outlook once it has escaped the precincts of the temple and spread to the bazaars-where reading and writing services were generally available, and even those who could not personally read did receive verbatim the contents of written announcements and even of popular books. Letters can form the outlook of a population even more intimately when literacy has reached the family level: that is, when in most families at least one member can read. Even in the villages a significant degree of literacy existed. In the towns, at least in some classes, literacy at the family level was probably common. (Note that general urban literacy at the family level might be indicated-in terms of statistics of a modern type-by a 'national' literacy level of ten per cent-i.e., twenty per cent of all males.)