The simplest answer is that the Confederacy had poor logistics for invasions everywhere in the war. Its armies had to be invented from scratch, which was a big part of the problem, but far from the only one. To defend in military terms is always easier than attacking. To raid is different from an invasion to conquer, which is what Sibley was actually doing. The New Mexico campaign was poorly structured from the start, relied on a logistical shoestring, and on the free and happy neglect of logistics that characterized so much of the defect of the Rebellion's generalship at its worst.

More than other subtypes of war, desert war places a premium on logistics and organization, both of which Sibley was massively defective in doing with even a modicum of competence. He made no effort to protect the logistical baggage train that sustained a War of the Rebellion army, which was a vital but unglamorous part of war at that time. It was the kind of oversight that with better generals than average for either side should on paper have killed a lot of offensives as dead as it did his (and in Virginia, at least, this is a good chunk of why US offensives in the first few years kept grinding to a halt). In the blazing wastelands of New Mexico the same oversight was far more fatal, to the lives of his men and even moreso to his reputation.

The irony of this is that his campaign and his approach up to Glorieta appeared to be a success on paper. He was able to march his army north, keeping that supply line clear, which in that condition in that point in time was no small feat. He was able to successfully outmaneuver the initial forces sent against him, with the start of the campaign at Fort Craig illustrating the faults that would culminate at Glorieta.

Sibley sought to maneuver the US Army into a battle at the time and place of his choosing, but the US Army, as war has a way of ensuring becomes the case, did not see the need to oblige him by giving him what he wanted on his terms. This led the Confederates to try to ouflank the US Army's main base at Fort Craig, by maneuvering to Valverde Ford. The US Army tried to attack him in turn, but the attack at Valverde was mismanaged, and the Confederacy managed to force the US Army into Fort Craig.

The cost of the victory at Valverde illustrates the point of Sibley's failure (and the Confederacy's army more broadly) at the elements of war beyond tactics. His army lacked the ability to recoup cavalry losses, and had no means to protect or care for its wounded, meaning that the wounded were pulled along with the army, which in turn slowed it down and left it to a crawling pace. Sibley was able to gain terrain, including the cities of Albuquerque and Santa Fe, but his pace meant that he was incapable of gaining any advantage beyond stretching his already-thin forces thinner than they already were.

This all took time, and by the time that battle was won, the reinforcements of Cols. Slough and Chivington, later infamous for Sand Creek, showed up. In a pattern that would recur in other campaigns and with other, much better equipped and informed armies, Stough interpreted directives of the actual commanding officer (Canby) in a way they were never meant to be interpreted, and decided to launch the Battle of Glorieta Pass, while Colonel Chivington went for the inglorious yet vital element of targeting Sibley's vulnerable and unguarded supply line.

Stough was tactically beaten at Glorieta as Canby's troops were sound on tactical issues and Stough had only a 200 troop margin of superiority. Stough chose to launch an attack on the basis of poor intelligence, which backfired spectacularly when a group of Texas he assumed were further forward than they were proved not to be, and the ensuing battle proved ferociously fought and a masterpiece of mutually poor combat direction in a pattern akin to that of Pittsburg Landing. Both sides had points of local advantages but the losses sustained in the local advances were beyond the power of either side to fully repair. The Confederacy was able to do so just enough to clear the pass, at the cost of leaving its supply lines unguarded.

Chivington, aided by a set of ethnic Mexican guides working with Lieutenant Colonel Chavez, a former opponent of the US Army in the Mexican War, recognized that the baggage train (read the entire logistical element that sustained the already-tenuous campaign up to that point) was unguarded and stormed out to burn it and destroy it, having as high an old time doing it as JEB Stuart and Stonewall Jackson would do to the Union Army in Virginia.

All war is a matter of logistics, and if a campaign mismanages this, it can win all of the battles but march an army to its destruction. See Bonaparte, Napoleon and the War of 1812. The destruction of the baggage train meant that in a single stroke, Sibley's logistical support was kaput and he had nowhere to forage to sustain the army instead, as Grant and Sherman would do later in the war, even if he wanted to. So he was forced to retreat, not because he fought the battles poorly, but because the failure of his generalship, and the Confederacy more broadly, to care about the sides of war beyond battles meant that the cumulative defects were beyond his power to repair, or that of his campaign.

Correspondingly, the US Army did not cover itself in glory, or demonstrate adeptness in tactics or the battlefield side of the war. Valverde was pitifully conducted, Glorieta was equally poorly managed from the US side. Tactics were over-aggressive, taken without full appreciation of the battlefield or measure of the enemy, and in both cases the US forces were soundly beaten at the tactical level. Victory was ruinous at Valverde, and the destruction of the logistical supply base of Sibley's entire expedition, not the actual tactics of Stough's forces, is what salvaged the campaign for the US Army.

The equal mismanagement of the retreat through the desert amplified this, though the USA did not exactly rush to pursue Sibley's army, due to its own logistical feebleness to conduct a drive into the desert.

Sources:

https://www.amazon.com/Sibleys-Mexico-Campaign-Martin-Hardwick/dp/0826322778

https://www.amazon.com/How-North-Won-Military-History/dp/0252062108

I would argue that the advance was actually not going as planned, as much as Sibley claimed it was after the tactical victory at Valverde and the later capture of Santa Fe. Despite holding the field at the end of the Battle of Valverde, Sibley failed to capture Fort Craig, leaving a well-armed, well-supplied enemy force on his supply route, and the battle cost his force most of their horses. When they took Albuquerque, they found all the Union stores destroyed, which forced them to acknowledge the fact that living off the land was difficult at best in the extremely arid environment that was (and is) New Mexico. Sibley thought that New Mexicans would welcome them "with a sincere and hearty cooperation"; he didn't seem to realize that stealing food, and sometimes women, from local farms would not endear them to a population who were somewhat predisposed to disliking Tejanos in the first place. They had imagined that they would be welcomed as liberators in New Mexico (assuming to encounter Hispanic citizens harboring an anti-Federalist mentality after the conquest of 1846), and most definitely were not, especially as the "living off the land" policy forced them to appropriate more and more food from the locals. The further north they got, the worse the situation became, as word spread and families fled with what goods they could carry in anticipation of their arrival (this had been happening since even before Valverde). When they "took" Santa Fe ("took" because it was deserted) they likewise found the stores at Fort Marcy either destroyed or moved to Fort Union.

Furthermore, after the defeat at Glorieta (where the Army of New Mexico lost most of the rest of their horses and mules, not to mention their entire 80 wagon supply train; Sibley wrote to the Texas governor, "We have been crippled"), they faced the Colorado volunteers coming from the north, and Canby's force threatening them from the south. After Canby heard of the victory at Glorieta, he feinted at Albuquerque, forcing the Confederates to flee Santa Fe to protect the last of their meager supplies, and then Canby and Chivington combined forces east of the city. Once that happened, it was clear to all that another battle would utterly ruin the hungry, unmounted, low-on-ammo Texans - they simply couldn't afford to sit and wait for reinforcements to make an uncertain trip northwards from Texas. The troops at Fort Craig also would have been just as big an impediment to any reinforcements as they were to Sibley; maybe even moreso since the reinforcements would have been traveling over the same route that had already seen its resources depleted, and locals enraged, by Sibley's men.

Sibley would claim that it was "the famished country that beat us", which is exactly what Canby had been counting on. Having served for years in New Mexico, he knew it simply couldn't support such an invasion force, especially without local support and with his men harassing their flanks and torching any Union depots that were likely to fall into Texan hands. In fact, he essentially declined to force a climatic confrontation since he knew he would be unable to properly care for the large numbers of wounded and prisoners that would be the inevitable result of such a battle, and he was content to simply let Sibley limp back to Texas. This move was not popular among soldiers on either side: Texans thought the campaign would have gone differently had they had proper Texan leadership (Sibley was from Louisiana, and was a notorious drunkard), and the Union forces hated watching their weakened foe escape without being allowed to finish them off. "We do not want to take any unfair advantage of the Texans - that would not be chivalrous," wrote one of the Colorado volunteers. "God grant they may never get the same advantage over us."

Conclusions and quotes drawn from Martin Hall, Sibley's New Mexico Campaign; John Taylor, Bloody Valverde: A Civil War Battle on the Rio Grande; Charles Carroll and Lynne Sebastian, eds., Fort Craig: The United States Fort on the Camino Real; Thomas Edrington and John Taylor, The Battle of Glorieta Pass: A Gettysburg in the West; Hampton Sides, Blood and Thunder