(Reviving an old thread ...)
Three examples of "magical problems" (or "supernatural problems" to use your term) that I an think of in literature are:
- The prophecy in about the Witch-King in The Lord of the Rings that "no man may slay him" (and his apparent invulnerability in general)
- Similarly, Achilles' invulnerability in Greek myth.
- And the endless supply of enemy troops produced by the Black Cauldron in the Chronicles of Prydain.
And there are many others throughout the corpus of fantasy fiction.

What's important, I think, in our writing is that we can have "supernatural problems" or "supernatural solutions," but not both together---in either case both problem and solution have to be well-developed, but if both problem and solution are "supernatural" or "cobhaic" it's hard for the reader to relate, and it can seem, as you say, too easy and a matter of authorial fiat rather than logical development. (Unless the "magical problem" is just one of the complications and dealt with mostly in passing.)
If we set up a "supernatural problem" that has a natural (i.e. non-magical / not "supernatural") solution, we can describe various "magical" and natural attempts to solve it to make clear that it's not "that easy." And if the problem is a "natural" one, we can show that
all "natural" solutions that the characters could attempt will fail, leaving the opening for something beyond nature. But if both problem and solution are "magical" or "supernatural," subject to laws that the author invented and usually doesn't reveal in full, this can feel more like a puzzle-style mystery with clues missing.