I was having the same problem (also with epubs as well as pdfs).
I went to Settings > Books > Online Content and Privacy and clicked on "Reset Access to Online Content"
This seems to have fixed the problem for now.
I also turned on a setting that says something about downloading from other devices.
I download everything directly to my ipad (not to icloud) and wondered if that might be related, so before I did the above in settings I moved the file I wanted to icloud and tried to download from there.
Somewhere in the midst of changing each of the above and then checking in Books, the download appeared and when I tried another file it no longer said "Importing Failed" . . . so something worked . . . or it was just waiting and opening and closing like another responder indicated.
In any case, I agree it's frustrating and that no matter what options I choose it sometimes doesn't seem to work, . . . and it certainly doesn't work as seamlessly as it should!! . . . but the above are a few other things to try.
And if anyone actually knows what each of these various settings is SUPPOSED to do (and whether it might be related to this bug) please let us know!