the birds wouldn't revert back to what they were
Since the example you have given implies an obligate nut eater a rapid decline in the population of it's food source would, indeed, cause a rapid decline in the population of the bird. A rapid extinction of the tree would similarly cause a rapid extinction of the bird which would preclude genetic evolution since that requires generational changes.

Taking your example we know that a nut eating bird has a very powerful bill - but if they were to be studies carefully variations in the size, density and mechanical strength, (the qualities required for the bill of an obligate nut eater), would most likely be quite apparent. The birds with the biggest, hardest and strongest bills and musculature to utilize the bill would be considered to be the best evolved - the fittest - while those with the smallest, softest and weakest bill the least well adapted. The second group is least likely to garner the lions share of the nuts because the better adapted specimens would be able to better harvest their food. In this case even the slow decline in the population of nut trees to the point of extinction would cause the extinction of the birds too.

This is the problem that any species that "forces itself into a corner" faces. They become so specialized that they become obligate and therefore rely entirely upon a single facet of their environment. Often only the smallest change in that environment would signal that species extinction. However, often the most successful species, (dietarily), are those that are omnivorous which, by definition, diversifies their diet and leaves them less susceptible to small environmental shifts.