When we talk about the elves "fading", we mean something very specific: the weakening of their bodily forms, and the subsumption of them by their spirits:
As ages passed the dominance of their fëar ever increased, 'consuming' their bodies (as has been noted). The end of this process is their 'fading', as Men have called it; for the body becomes at last, as it were, a mere memory held by the fëa; and that end has already been achieved in many regions of Middle-earth, so that the Elves are indeed deathless and may not be destroyed or changed.
History of Middle-earth X Morgoth's Ring Part 2 "The Second Phase" Chapter 3: "Laws and Customs Among the Eldar" Of Death and the Severance of Fëa and Hröndo [> Hröa]
On some level, all of the Ainur1 are susceptible to this effect, but in the most vacuous way possible: since they can shed their bodily forms as easily as an incarnate might shed a coat, they can very easily subsume their physical form, but it doesn't really mean the same to them as it would to an Elf or Human; they can just create another one. There's no reason to believe that this kind of involuntary fading would affect them.
That being said, it's more likely that it would have occurred to someone like Radagast who, though Ainur by nature, was tied to a body in similar manner to an incarnate and could be "killed." However, since Tolkien never wrote about the fate of Radagast, we can't be certain. I would presume that other "incarnate" Ainur, like the balrogs, would also suffer a similar fate in the end.
However, the Ainur do "fade" in a different way: they become less potent, and less able to effect material changes in the world. But this is an effect of the passage of time, not of Middle-earth or Arda Marred, and affects them even in Aman:
The Valar 'fade' and become more impotent, precisely in proportion as the shape and constitution of things becomes more defined and settled. The longer the Past, the more nearly defined the Future, and the less room for important change (untrammelled action, on a physical plane, that is not destructive in purpose). The Past, once 'achieved', has become part of the 'Music in being'. Only Eru may or can alter the 'Music'.
History of Middle-earth X Morgoth's Ring Part 5: "Myths Transformed" Chapter VII "Notes on motives in the Silmarillion" (iii)
1 Those not tied to a specific physical form, that is.