Surely one assumes after 7 centuries of Muslim rule they would've started speaking Arabic.
Edit: thanks for the answers. The consensus seems to be that Arabic didn't take hold because it was the language of the elites, and because it was too different from Spanish in the first place.
Piggy back question: Is the influence of Arabic and Mozarabic responsible for the distinctive features of Andalusian Spanish or are they just independent innovations?
The I'm a little late to the party, but I think I may contribute a slightly different perspective. I am not sure I agree with the contention that Arabic did not catch on because it was too different from the Vulgar Latin, proto-Romance languages it encountered in the peninsula upon its arrival in the early eighth century. In the late medieval period, many in the Nasrid kingdom of Granada and even Valencia were native Arabic speakers, and it is only with the final conquest of those kingdoms that spoken Arabic begins to decline. Arabic literary culture and even the language were stifled in the late medieval and early modern periods. The expulsion of the Moriscos in the 17th century certainly did not help the language's survival chances.
It is important to remember that culture and language tend to spread slowly, and in an agricultural society like early medieval Spain, it is not all that surprising that Arabic was not firmly entrenched when the Christian kingdoms began their southward expansions. It is even unlikely that the recently conquered Berbers who invaded with the Arabs were native Arabic speakers at this point! Conquests in the early medieval period typically did not involve massive migrations of people, and while they would become the ruling class, Arabic speaking immigrants represent a minuscule fraction of medieval Iberia's population following the conquest. Settlement was sporadic and tended to focus on urban centers; the rural regions of al-Andalus, populated by speakers of what would later become the Mozarabic language, were in many ways culturally isolated from high Arabic culture.
That being said, Arabic would begin to work its way into Andalusian society. It would be incorrect to say that Arabic was simply an elite language in medieval Spain. As the lingua franca of medieval al-Andalus, it was not just the language of politics and high culture, but it was also the language of commerce and trade. Even among the Mozarabs there is evidence of bilingualism and there was likely a widespread, working knowledge of Arabic. We even have a ninth century letter complaining that Mozarabs were more proficient in Arabic than Latin!
Linguistic diversity is the rule rather than the exception in early medieval societies, and coordinated efforts to impose the language of the conquerors onto their new subjects is rare to nonexistent. Language adoption occurred naturally and in many cases, slowly among the rural majority population of Al-Andalus. In regions where Arabic was never spoken natively, it lost its status as a prestige language and fell out of use. In regions where it had become more entrenched, linguistic repression and the expulsion of those most likely to speak the language natively hastened its demise. That is my take at least. I am less familiar with the early modern period at which your question is directed. Perhaps another flaired user, such as /u/Itsalrightwithme, can clarify or correct anything I have written. I do hope, however, that I have provided some important context on the state of the Arabic language in medieval Iberia.
Edit: grammar and minor mistakes