Moving the goalposts
Moving the Goalposts is a type of informal logical fallacy in which the arguer, presented with evidence against one of his claims, redefines his claim without acknowledging the validity of the evidence and counterargument.
The argument is a fallacy since it redefines the claim as needed to suit the argument. In doing so, it can make any claim at all vacuously true and invulnerable to reasoned disproof. No True Scotsman is a particular example of this kind of fallacy at work, where the definition of a word is illegitimately shifted to exclude undesired examples.
Antagonist: "That movie reviewer is clearly biased; no foreign film has ever gotten more than two stars from him." Protagonist: "Actually, I think Crouching Tiger, Hidden Dragon got three and a half when it came out." Antagonist: "Yes, well, He's never given four stars to any foreign film." Protagonist: "I think he gave four stars to No Man's Land, too." Antagonist: "Well, those were both Oscar winners. He has to rate those highly. But he's never given four stars to any foreign film that didn't go on to win an Oscar."
Antagonist: "Evolution is clearly impossible; no life form can change" Protagonist: "Um, livestock breeders do it all the time. Where do you think hybrid roses come from?" Antagonist: "Well, that's just microevolution. You breed a new rose, it's still a rose. What you can't do is breed a new species." Protagonist: "Actually, we can and have. There's lots of examples of observed speciation. Antagonist: "Yes, but you still just get another variation of the same kind; you never get a completely new type of animal. You can't breed a dog and get a chicken."
The key to understand this fallacy is to understand what a claim under discussion actually means. In most cases, the actual "claim" is a relatively broad and perhaps ill-defined one. What does it mean for a movie reviewer to be "biased"? In most cases, the person making such a claim will have an intuitive, informal idea of what he really means, but cannot necessarily articulate the exact evidence upon which he bases his idea. I might, for example, think that a reviewer is biased because he consistently rates foreign films lower that I do, but I (mostly) agree with his ratings of domestic ones. That's hard to articulate and even harder to demonstrate, but it may nevertheless be real.
On the other hand, "moving the goalposts" can also be a sign that the claimant has made up his mind and is impervious to evidence. If he is convinced, for example, that a pattern exists, any single counterexample can be dismissed as unrepresentative.
Exceptions to the Rule
"Moving the goalposts" can be legitimate when used to make more explict exactly what is meant by a given claim, as in the film review discussion above. When the proposed amendment to the claim is more accurate and useful than the original claim, then moving the goalposts is simply an intelligent response to valid criticism.
Also, claims of "moving the goalposts" often degenerate into mere semantic quibbles when the overall meaning of the statement is clear. For example, a claim that "all scientists today accept the theory of gravity" is probably false in detail. If you spent the next five years searching assiduously, you could probably find a single person, somewhere in the world, with training in science who holds a contrary opinion in the teeth of near-universal disdain and all standards of evidence. Focusing on the lone holdout adds legitimacy to an otherwise nonexistent controversy.