Biologist here with a PhD in endocrinology and reproduction of endangered species. I've spent most of my career working on reproduction of wild vertebrates, including the panda and 3 other bear species and dozens of other mammals. I have read all scientific papers published on panda reproduction and have published on grizzly, black and sun bears. Panda Rant Mode engaged:

THERE IS NOTHING WRONG WITH THE GIANT PANDA.

Wall o' text of details:

    In most animal species, the female is only receptive for a few days a year. This is the NORM, not the exception, and it is humans that are by far the weird ones. In most species, there is a defined breeding season, females usually cycle only once, maybe twice, before becoming pregnant, do not cycle year round, are only receptive when ovulating and typically become pregnant on the day of ovulation. For example: elephants are receptive a grand total of 4 days a year (4 ovulatory days x 4 cycles per year), the birds I did my PhD on for exactly 2 days (and there are millions of those birds and they breed perfectly well), grizzly bears usually 1-2 day, black bears and sun bears too. In the wild this is not a problem because the female can easily find, and attract, males on that 1 day: she typically knows where the nearest males are and simply goes and seeks then out, or, the male has been monitoring her urine, knows when she's entering estrus and comes trotting on over on that 1 day, easy peasy. It's only in captivity, with artificial social environments where males must be deliberately moved around by keepers, that it becomes a problem.

    Pandas did not "evolve to die". They didn't evolve to breed in captivity in little concrete boxes, is all. All the "problems" people hear about with panda breeding are problems of the captive environment and true of thousands of other wild species as well; it's just that pandas get media attention when cubs die and other species don't. Sun bears won't breed in captivity, sloth bears won't breed in captivity, leafy sea dragons won't breed in captivity, Hawaiian honeycreepers won't breed in captivity, on and on. Lots and lots of wild animals won't breed in captivity. It's particularly an issue for tropical species since they do not have rigid breeding seasons and instead tend to evaluate local conditions carefully - presence of right diet, right social partner, right denning conditions, lack of human disturbance, etc - before initiating breeding.

    Pandas breed just fine in the wild. Wild female pandas produce healthy, living cubs like clockwork every two years for their entire reproductive careers (typically over a decade).

    Pandas also do just fine on their diet of bamboo, since that question always comes up too. They have evolved many specializations for bamboo eating, including changes in their taste receptors, development of symbiosis with lignin-digesting gut bacteria (this is a new discovery), and an ingenious anatomical adaptation (a "thumb" made from a wrist bone) that is such a good example of evolutionary novelty that Stephen Jay Gould titled an entire book about it, The Panda's Thumb. They represent a branch of the ursid family that is in the middle of evolving some incredible adaptations (similar to the maned wolf, a canid that's also gone mostly herbivorous, rather like the panda). Far from being an evolutionary dead end, they are an incredible example of evolutionary innovation. Who knows what they might have evolved into if we hadn't ruined their home and destroyed what for millions of years had been a very reliable and abundant food source.

    Yes, they have poor digestive efficiency (this always comes up too) and that is just fine because they evolved as "bulk feeders", as it's known: animals whose dietary strategy involves ingestion of mass quantities of food rather than slowly digesting smaller quantities. Other bulk feeders include equids, rabbits, elephants, baleen whales and more, and it is just fine as a dietary strategy - provided humans haven't ruined your food source, of course.

    Population wise, pandas did just fine on their own too (this question also always comes up) before humans started destroying their habitat. The historical range of pandas was massive and included a gigantic swath of Asia covering thousands of miles. Genetic analyses indicate the panda population was once very large, only collapsed very recently and collapsed in 2 waves whose timing exactly corresponds to habitat destruction: the first when agriculture became widespread in China and the second corresponding to the recent deforestation of the last mountain bamboo refuges.

    The panda is in trouble entirely because of humans. Honestly I think people like to repeat the "evolutionary dead end" myth to make themselves feel better: "Oh, they're pretty much supposed to go extinct, so it's not our fault." They're not "supposed" to go extinct, they were never a "dead end," and it is ENTIRELY our fault. Habitat destruction is by far their primary problem. Just like many other species in the same predicament - Borneo elephants, Amur leopard, Malayan sun bears and literally hundreds of other species that I could name - just because a species doesn't breed well in zoos doesn't mean they "evolved to die"; rather, it simply means they didn't evolve to breed in tiny concrete boxes. Zoos are extremely stressful environments with tiny exhibit space, unnatural diets, unnatural social environments, poor denning conditions and a tremendous amount of human disturbance and noise.

tl;dr - It's normal among mammals for females to only be receptive a few days per years; there is nothing wrong with the panda from an evolutionary or reproductive perspective, and it's entirely our fault that they're dying out.

/rant.