To my knowledge, the Cordoban Islamic state was much more advanced then it's christian neighbors in northern Hispania. Economically, it was an urban cash economy, whereas the christian states had feudal economies. It was also a very urbanized society, and considered to be one the wealthiest states in Europe. Cordoba even had the largest population of any city in Europe at one point. I don't like using this word, but I did see some people on this sub call the economy and society of the northern Christian states "backward". Yet, in the 8th and 9th centuries, I see the Christian states expanding southward. Even in the 10th century, at the peak of Cordoba's prosperity, the Christian states seemed to be the ones doing the expanding. Why was this? If Cordoba had such an advanced society, how come it was never able to military conquer it's opponents? From what I know, the northern Christian states were only ever able to field very small armies. At the Battle Of Sagrajas, the Christians had about 3,000 soldiers. At the battle of Fraga, about 2,500. At the battle of Ucles, 2,300. And these battles all took place after Cordoba's peak in power. It makes sense that these states would have only ever been able to field about 3,000 men in any battle against the state of Cordoba, while Cordoba could likely field 10,000+ if it just created an army of levies from only Cordoba. So why was Cordoba never able to conquer the Christian states of Northern Hispania?
Three reasons. Centralization and politics, geography and tactics, and allies and actual fighting.
Let's begin with the easiest. Those regions of Spain, the Cantabrian Mountains, the ones in the north of Spain, are very wet and mountainous. It is incredibly hard to get a big army through there. Think of the Vietnam war without air support. That directly led to the tactics used by the early Christian nobles, and later the Asturias - they utilized raiding and guerilla warfare, which meant that they were impossible to defeat in a single battle. Also, that type of terrain made it very hard to take advantage of numerical and economic superiority over the enemy - 300 men can block a path for 10000 and delay them long enough for the logistical problems of feeding and defending a column of 10000 men to appear. All of this made the brute force approach to the problem ineffective. In fact, during the 10th-beginning of 11th century (929-1002), the muslim Umayyads tried using that approach to put an end to the Reconquista, with moderate success - it was simply too late.
Next, the politics and centralization. Originally, Spain was conquered by the Berbers from Africa, who had problems in the african homeland. The actual Iberia wasn't centralized at all, with the governors constantly plotting revolt, and actually breaking up into a civil war between 1002 and 1031, which resulted in the appearance of like 30-35 incredibly tiny so called Taifa kingdoms, each of which betrayed the others without any concern for the christian threat. On the other hand, the Christians were unified under one banner of Leon/Asturias against the Muslim threat they considered existential, and didn't start infighting until 1063, when the Muslims were already broken up. The infighting was over and the Christians made gains by the time the Almoravids arrived and unified the Muslims again in 1086, and from there it was already a lost campaign for the Muslims. Also, in case of infightings, the Christians had the Pope as the final arbitor of any disputes heavily on the side of achieving the Reconquista.
And finally, allies. The Christians didn't have to endure all the fighting on their own - they had allies. Like the Franks, for example. In fact, for much of the 8th century the Muslims were fighting the Frankish threat right across the Pyrenees. The logistics were hard and the Muslims had to retreat, and the Franks pursued them over the Pyrenees, reconquering and supporting Catalonia and what was soon to be Aragon and Navarra. The Muslims, on the other hand, had to fight basically a two-front war against these enemies all on their own, with the only, unreliable, allies in the face of Berbers who constantly had to go back to Africa.
TL;DR: well they tried, but it's hard to win a two-front Vietnam war.
Loosely based on:
O'Callaghan, Joseph F. (2003). Reconquest and Crusade in Medieval Spain. Philadelphia: University of Pennsylvania Press.. ISBN 0812236963.
Collins, Roger (1989). The Arab Conquest of Spain 710–797. Oxford, UK / Cambridge, USA ISBN 0-631-19405-3.
Edits: fixed some grammar and typos here and there, added a date