In short, the US government had a slightly bigger problem on its hands, with the whole 'engulfed in Civil War' thing going on, and it pushed any opportunity for the continuation of the U.S Camel Corps to the wayside, although to be sure, there wasn't much momentum behind it to begin with. The small successes up to then demonstrated, especially the expedition under Ed Beale, might have proved their value, but it was nothing more than a proof of concept. The suggestion to "purchase 1000 camels" which you reference wasn't exactly being acted upon. Beale had advocated strongly in favor of more camels in his 1858 report, and John B. Floyd, then the Sec. War, made that proposal to Congress, but it was fairly well ignored, despite being repeated again by Floyd in 1859 and 1860. Beale continued to utilize the animals in surveying out in California, but that was the extent of things by 1861, and then whatever chances there might have been to turn Congress around vanished with secession. The exigencies of wartime thus put a hard stop on further expansion of the program, and even the best advocates of the program - Beale, and Maj. Henry C. Wayne who oversaw the initial acquisition and got the program rolling - were hard-pressed to give it their attention (and also Jeff Davis, no longer giving his allegiance to the US at all!).

For the existing camels, they had a mixed fate. Despite the praise of Beale, who was quite right that well cared for, camels could be excellent tools, it wasn't the universal experience. An 1860 attempt to use camels between LA and Fort Mojave was a disaster - the camel ridden by Capt. Hancock to test the route died of exhaustion - and likely put a damper on interest by those not already converted to their merits. For the camels which had previously been part of the Beale expedition, in 1861 they were moved to San Pedro, CA where they were used, for a time, to carry cargo to nearby Los Angeles, but not much else. Beale in that time did attempt to push the government into using the animals more effectively, and even offered to take possession of them under bond, but for whatever reason, the government wasn't interested in his offer.

In 1863, there was one final attempt to utilize this group as long-distance transportation, traveling to Tucson, AZ, but the results were unsatisfactory, and the next year they found themselves auctioned off, purchased by Samuel McLaughlin, who had been their caretaker at that point. He used some to haul freight between California and Nevada, but others he apparently sold off individually, mostly as curiosities.

Those camels based in Texas however fell into Confederate hands - another impediment at continued use by the US Army of course - but for the most part there was little interest in the animals by the Rebs, who knew nothing about their use or care. Many escaped and wandered aimlessly - some to be recaptured by the Union, but wild camels would continue to be spotted for the next half-century - and those that didn't were often ignored and neglected. Very few seem to have actually been used as pack animals, and then, mostly on personal initiative, by random soldiers, although at least a few were used to transport cotton south to Mexico to evade the blockade. The Union recaptured the remaining stock in 1865, and they too were auctioned off. Whatever lessons might have been learned in the pre-war years about the camels' utility was apparently lost, and a Col. Coopwood bought the animals at 31 dollars a piece, taking them into Mexico a year later as part of an unsuccessful venture at carrying mail between there and the US. Reports seem to be that they mostly ended up in circuses.

Uncle Sam's camels; the journal of May Humphreys Stacey supplemented by the report of Edward Fitzgerald Beale (1857-1858) edited by Lewis Burt Lesley

The Last Camel Charge: The Untold Story of America's Desert Military Experiment by Forrest Bryant Johnson

Perinne, Fred. "Uncle Sam's Camel Corps". New Mexico Historical Review, Vol. 1, No. 4 1926 434-445

As an additional note, it doesn't seem to be digitized, or at least my library doesn't make it so available, but "The U.S. Camel Corps : an Army experiment" by Odie B. Faulk seems to be the most in-depth treatment of the topic, and certainly is well reviewed based on what I did turn up:

Greever, William S. Pacific Historical Review 46, no. 3 (1977): 502-03. doi:10.2307/3637519.

Kroeker, Marvin E. The Journal of American History 63, no. 3 (1976): 728-29. doi:10.2307/1887406.

Edit: Formatting

Edit II: FYI it is passed my bedtime, but I'll try to answer follow-ups tomorrow.

Hello everyone,

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Follow-up: Were there any major differences between the deserts of the SW United States and those of the Middle East and North Africa (from which the camels in question were presumably imported) that made it difficult for them to adapt?