Sometimes, PDFs and downloading aren't two words that go well together on the iPad. It's the way the PDF is, or the web site is, or both. I, personally, have not had the trouble you describe, however...
That said, I've discovered an app called Download with Dropbox ($1.99, USD). With it, I can download stuff right off the Internet and put it directly into Dropbox. The app is basically the "middleman" between the Web and Dropbox.
I have no affiliation with the app - it's just what works for me. Maybe give it a shot?
Or, do you have the Goodreader app ($4.99, USD)? If so, try putting a "g" in the very front of the URL (if it ends with .pdf). That should open the whole thing up in Goodreader (and save it, also).
Or, some of the browsers [Atomic Web ($0.99, USD) and iCab ($1.99, USD)] being two that I know of) can also download PDFs. Maybe you have those and can try them?
Hope some of this gets you to your download. Good luck and let us know how you get on.
Marilyn