In Harry Potter and the Goblet of Fire, Dumbledore has appointed Alastor Moody as the D.A.D.A. teacher and, of course, we find out that was not Moody, but was Bartemius Crouch pretending to be Moody for that year and that Moody was prisoner during that time.
The next year Delores Umbridge takes up the position of D.A.D.A. teacher. According to this question, Umbridge was only hired after Dumbledore was unable to find a suitable candidate for the position.
One year before, Moody was hired, clearly showing he would be an acceptable person for the position. He, however, never actually held the position due to Crouch's impersonation of him.
How come Moody was a good choice and willing to take the job for that school year, but a year later, he apparently isn't even a candidate for the position? Clearly he was qualified and wanted for the job before. Why would Dumbledore not consider him a good choice a year later?