“An organism is unable to return, even partially, to a previous stage already realised in the ranks of its ancestors.” Louis Dollo.
The idea that once lost, an organism could never again re-evolve a given trait was quite prominent in the early 20th century but has now largely passed on into history. It may seem obvious now that this was a questionable assumption, but the fossil record was much more poorly known then (as indeed were the mechanisms of inheritance and variation) and the differences between many major clades were apparently much greater owing to the (then) missing intermediates (though of course something like Archaeopteryx was already much celebrated). While it does even now seem unlikely that feathers could evolve twice independently (though of course it’s just possible) the real reason that a character might vanish and then crop up again lies in genetics.
A simple point mutation (that is, a change to just a single base pair in the genome) could, potentially, eliminate an entire set of characters from appearing (like say the development of limbs or feathers) in the organism. This could then be reversed in a later generation with another single point mutation that restores the original state of the genome (assuming it has not mutated or altered further in the meantime). In practice of course, both scenarios are unlikely and the complete disappearance or reappearance of a character in a single generation are probably effectively impossible. In general the loss or gain of a feature (especially across a clade as opposed to a single organism, a featherless hawk might hatch from an egg, but that doesn’t make the species featherless) is slow and steady. More and more teeth might be evolved in the jaw over generations until a descendant species has far more than the ancestor, but the number is unlikely to double immediately in one or a few select individuals and then spread very rapidly across the population. Since a great many (and probably most) traits are controlled by multiple genes and genetic and developmental pathways then there are of course a multitude of ways of say adding more teeth and indeed there are many ways of getting rid of them too.
Which returns us a little haphazardly to the original point of this post – character reversals, which are basically characters that seem to have gone from one condition to another during their evolution and later returned to the original state. Typically these reversals refer to the small and detailed characters that are used in systematic and phylogenetic work but can also relate to whole complexes. A good example would be the manual claws seen on the fingers of young hoatzin.
Clearly ancestral birds had clawed fingers (like Archaeopteryx for starters) and these were later lost as exemplified by, well, virtually every living bird and quite a few fossil ones. None of the other relatives or apparent ancestors of the hoatzin have these claws, so there is now way they have been hanging around for a long time unnoticed. Thus their return in these birds is a reversal of this character as it has been reacquired. Actually, ‘reacquired’ is perhaps not the best term to use, since the ability to produce claws was doubtless floating around unused in the genes of these animals. A better term would therefore be that these claws have been ‘re-expressed’.
The short message is though that these characters can and do change (evolution is, of course, not random but selected). You can see characters oscillating even in some circumstances such at the studies done on beak shapes in Darwin’s finches where successive droughts or wet seasons can prompt beaks to switch from bigger to smaller morphs and back again and back again over just a few generations as conditions favour one beak shape or the other.