I really hope Ghilly sees this post because I'm honestly not certain. No vet has ever given me such a caution after neutering surgery, so this is a new one on me! You might post your question on the Ask a Vet board here at Med Help. One of the veterinarians can certainly answer this question better than I can. :-)
It's about 90 days I think, that the male dog would still be able to sire pups after neutering. I think it is something to do with residual sperm (though how they live that long is, to me, a mystery)
I know a male dog who was neutered about 5 years ago. He is still capable of mating fully, though of course he would not now be fertile. But he can certainly do it! So it seems there is still some testosterone in his system, even though he's 'firing blanks'!
After neutering, testosterone levels drop off over 30-60 days, and the urge to breed goes with it. However, as far as having viable sperm goes, a dog can have viable sperm for as long as 4 - 6 weeks after neutering, so it's wise to make sure he doesn't get near any breedable females in that time.
Some dogs will be able to breed females their whole lives, even after neutering, but these dogs are the exception and not the rule, and naturally the females will not become impregnated, but the males will give it the old college try. :)