I heard yesterday that female pandas are on heat for only 3 days a year.  What could be the evolutionary benefit of this?  Alternatively, how have they managed to survive this long?  Have female pandas somehow become less productive?  And if so, why?

And if pandas are so difficult to breed, would that not suggest that the logical evolutionary solution would be extinction?  Is it purely down to habitat?

BTW, I'm sure you've seen it, but in case not, do have a look at "sneezing panda" on youtube!  :)

Well the evolutionary benefit of making sure you only have offspring at a particular time of year could be of enormous benefit if timed to fit well with the part of the year when food is most readily available etc. so there isn't necessarily a negative to only being in heat at a set time, it can under the right conditions be a positive.
The notoriety of pandas being difficult to breed comes from human attempts to breed pandas in captivity. At first being unaware of the idea that they went into heat (as there are few physiological clues that can be detected simply by observation), and afterwards making sure that the pandas are put together at the right time (for the same reason, few if any observable signs), currently I believe they take regular urine samples to test for hormones. Unfortunately male and female pandas cannot be housed together when the female is not in heat, as they are highly territorial and prone to fighting.
In the wild however, pandas enjoyed (or they used to before much of their habitat was destroyed) vast territories where they would wander over many miles in solitary. However when a female went into heat, the male pandas excellent sense of smell makes it relatively easy for them to detect it and track the female down. So in their natural habitat pandas have no problem reproducing, there major problem is the destruction of their habitat, which is reducing the numbers of pandas it can support, and isolating them from each other via human interference (settlements, farmland etc.)

Thank you for the sneezing panda :)

last I heard, using hormone tests the panda conservation program in China has huge success. Pandas can do these tests by smell, so I guess "in nature" their success rate used to be high, too ;)