Some critiques of the question you're asking before we start answering it.

It's inaccurate to use the term "Christian reconquest" as some sort of blanket term for lands that were at one point ruled by Muslims but are no longer. The premise that certain lands are inherently "Christian" is problematic. There were Muslims living in the Crusader Kingdoms, and there were Christians living in al-Andalus for the full duration of Islamic rule, for example.

Most of the examples you're citing here are lands that were colonized in the 19th century. European colonialism in the Islamic world was not an attempt at 'reconquest' (except possibly Algeria, which France annexed, but even then it was never portrayed as any form of reclaiming territory but rather annexation of new territory); there was no intent to rule those lands indefinitely, nor to push out the existing populations (as happened in Iberia--again, with the exception of Algeria), nor to convert them to Christianity (even in Algeria). Sicily was only under Fatimid rule for a brief period in the 12th century. Cyprus was colonized by the British, but there as in Crete the majority of the population were not Muslim. In Sicily and Cyprus the Muslims were not pushed out; in Crete they eventually were, but that's a complicated story about the conflation of Greek nationalism with Orthodoxy.

Also, 'Moor' is an outdated term. We're talking about Muslims of differing ethnic groups.

The reconquista was a very specific movement in Iberia to push out what were seen by Christian Europeans as a foreign population. Historically speaking, it only applies to the conquest of the emirate of al-Andalus by the armies of the petty kingdoms that eventually unified into Spain, which began in the 1000s (for reference, the Muslim armies crossed into Iberia in 711).

Even here, though, "reconquista" reduces Muslims to "invaders" of "Christian" lands. The Muslims came to settle in Iberia and ruled parts of it for over 700 years. (Think of it this way: the Native Americans still have two centuries to get their act together and throw out all of the European descended population from the Western Hemisphere.)

There was no country called 'Spain' before the Muslims arrived; after Roman rule, there were small petty kingdoms of people who spoke what was only just beginning to break down into Vulgar Latin (and centuries away from becoming early Spanish), ruled by the Visigoths, a Germanic speaking people who had themselves invaded in the late 5th century. The reconquista came out of the various kingdoms in the north of Iberia--Galicia, Aragon, Castille, Navarro, etc.--in the 11th century. They eventually became a unified population because they were fighting together (but even then it took a long time--properly speaking, Granada fell to the Kingdom of Castille and Leon, not to Spain as it hadn't yet unified). And they were, in fact, inspired to try by the Crusades -- one of the popes even blessed the reconquista as a Crusade (I have forgotten which one).

These armies were successful for a number of reasons, one of which is that they were fighting at home over an extended period of time--it took almost 400 years from start to finish. It wasn't a constant battle--nor, frankly, was it all enmity. There was plenty of trade and cultural exchange going across the border back and forth. But the failure of al-Andalus also involved internal strife within the emirate itself that weakened its military prowess.

Why were the Moors unable to reclaim Al-Andalus from the Iberian Christians while the Ayyubids and Mamluks were able to reclaim Jerusalem, Acre, Tripoli and Antioch (now Antakya) from the Crusaders?

Simply put, they never tried. There was no attempt to militarily re-insert themselves into Iberia after the fall of Granada in 1492.

The Crusades seemed like it would inevitably drive the Muslims out of the Holy Land for good.

Not really. They just weren't that successful. Yes, if you look at a map, it looks as though European kingdoms were set up in the region, but on the ground this wasn't the case--there was no widespread immigration coming from Europe to settle the region. You basically had a handful of European knights setting themselves up as nobility ruling over the people who were already living there (Christian, Muslim, and Jew). The initial success of the Crusaders in conquering the area--which was more the result of the disunity and disorganization of the Muslim kingdoms in the region than it was about any sort of technological or military superiority on the part of the Crusaders--wasn't matched by their ability to rule (remember, most of these guys were the third and fourth sons who had never been groomed to take over their fathers estates because it all went to the oldest son). The Crusaders weren't always that tolerant of the local Christian populations, either, since they tended to be Orthodox and this was right after the Great Schism separating Orthodoxy and Catholicism. Treating your subjects as the enemy when there's a sympathetic state right next door is usually a bad idea.

The Crusader states were geographically removed from Europe and required support from "home," which waned and faltered because "France" and "Italy" weren't unified kingdoms, nor were they wealthy enough to keep a constant supply chain going. There were attempts to shore up the Crusaders states by launching subsequent Crusades, but the majority of them never reached the Holy Land. It didn't at all help that the Crusaders had sacked the nearest Christian power (the Byzantine Empire--the seat of now-heretical Orthodoxy) and therefore required supplies and assistance from places further away--the Byzantines also weren't all that keen on allowing the Crusaders to cross their territory given their tendency to sack Byzantine cities, which made them more vulnerable to Seljuk and Ottoman conquest. Eventually they had to trade with their immediate neighbors, who got their act together and were able to push them out.

If you're interested, I would recommend Paul Cobb's The Race for Paradise as a primer on the Crusades from the Islamic perspective (he also discusses Sicily and Spain); seen from a different angle the whole episode takes on a much different appearance.