When things came to actually selling the book, however, we realized that something isn't working. While people who had read the book loved it, for the most part, the views/clicks rate on our Amazon ads was unsatisfactory. To put it simply, hardly anyone was clicking on to the book's Amazon page.
This led us to think that the cover, while perfectly fine in itself, does not quite fit the book. The cover, together with the title, might create a mistaken impression that this is a children's book - which it is emphatically not. We wanted something that would spell out "dystopia" more clearly, and give some sort of hint as to what goes on in the narrative. Finally, we decided on a new cover:
The girl against the background of the ruined city is quite representative of the plot, and the cover, overall, fits the genre better.
Once more, this incident makes me feel thankful for digital publishing and print on demand. Changing your cover or correcting mistakes is quite easy, simple and free of hassle. Authors and publishers can play around and see what works, what doesn't, and what just needs to be tweaked.
Also see Joanna Penn's excellent post on changing book covers.