I must say their continued rarity is something I have never really understood. As Alex said, they are super effective. They also have strong family bonds, and good breeding strategies (only the alpha pair breed, but the whole pack helps with the rearing) and large litters.
I understand that they have been heavily persecuted in non-game-reserve areas, but this does not explain why they remain so scarce now.
I have seen them only twice, once in the camp at Savuti.
They breed easily in captivity and reintroduction into reserves is also very successful.
So the answer to the riddle, I think, has to do with the pack size:
The behaviour of Wildogs are characterised by their reliance on 'helpers'. This includes cooperative hunting, defence from competitors for their prey (hyenas), pup feeding and baby-sitting. Because of this there is a strong positive correlation between pack size and the production and survival of pups. Consequently, a pack in which membership drops below a critical size may be caught in a positive feedback loop: poor reproduction and low survival further reduce pack size, culminating in failure of the whole pack (source: "Crucial importance of pack size in the African wild dog" - Courchamp & Macdonald, 2000).
I have seen a small group of four, after being reintroduced from breeding in the Madikwe reserve (that was 2001). This is a guided only reserve (no self-drive). The ranger at the time said that particular pack used to be 5 (adults only). Based on the above paper, I would think their chances of successfully increasing in numbers would have been small. So this poses the challenge of only reintroducing them to reserves once a sufficiently large pack size is reached in breeding. I do not know if this is actually being practised though.
MAybe that's the answer, because it would also mean that youngsters could not leave a pack to start a new one and the pack size is probably limited to the "carrying capacity" of their home range...