Alastor Moody does in fact appear once in Half-Blood Prince, at Dumbledore's funeral (my emphasis):
An extraordinary assortment of people had already settled into half
of the chairs; shabby and smart, old and young. Most Harry did not
recognize, but a few he did, including members of the Order of the
Phoenix: Kingsley Shacklebolt; Mad-Eye Moody; Tonks, her hair
miraculously returned to vividest pink; Remus Lupin, with whom she
seemed to be holding hands; Mr. and Mrs. Weasley; Bill supported by
Fleur and followed by Fred and George, who were wearing jackets of
black dragon skin.
The reason for his otherwise lack of appearance is probably that he was not present (or his presence was unimportant) at the various events portrayed in the story. Most of the book takes place at Hogwarts, where Moody would not be expected to appear. Even though Hogwarts is under the guard of aurors that year, Moody is an ex-auror; moreover, Harry rarely saw the aurors that were there anyway.
In the small part of the book that takes place elsewhere, even though we never see Moody we almost see him. When Harry arrives at the Burrow, we find out that Moody is coming for dinner on the weekend:
“Dear, why not come to dinner at the weekend,
Remus and Mad-Eye are coming — ?”
However, the weekend dinner is apparently not an important enough part of the story for us to actually see it. The same is probably true of other events where Moody would have been present throughout the year.