I'm not sure I can properly answer this question because its premise is flawed. There is considerable Arabic influence in the Spanish language. Hundreds of nouns are Arabic in origin--for example, chances are, if a noun starts with al-, it comes from Arabic. Tons of place names in Spain--and consequently Latin America--are derived from pre-Reconquista Andalusian names, particularly all the Guadal- rivers.
Now, Arabic had little effect on Spanish syntax and grammar, but that is very normal. English is another example of the same situation: we have tons of French and Latin vocabulary, but still a distinctly Germanic structure.
I'd like to just add and support what /u/alfonsoelsabio has written up. The influence of Arabic is still heavy in the south of Spain and particularly in Mexican Spanish. In fact, as was mentioned, words beginning with "Al" have almost always been Arabic in origin, and more specifically belonging to Arabic spoken by the Maghreb Arabs. Words like: Algodon/Al-kutun/Cotton, Alcova, Algebra and Alacrán are a small sample of this. Many scientific words and even the common acknowledgement "ojalá" (which comes directly from "inshallah" or "god willing") are very much in use today. To use another example, even the 1st division football team, Granada CF, is nicknamed "Los Nazaríes" in a nod to their heritage. The Alhambra (Al-ahmar in Iraqi Arabic), or the 'red one' is still recognized as one of pearls of Moorish architecture in Al-Andalus/Andalusia. Side note, some of my family is from Guadalajara, el río de piedras, the river of rocks.
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