The problems I was having were with the download servers of a specific pdf, in the end. During the same session, I was able to download a couple other pdfs without any problems. And finally, I got the pdf I wanted after a couple trys.
The thing with resuming the download after it fails, I used to be able to do that before, but now firefox doesn't seem to recognize the .part file anymore.
I dunno, I don't use annas-archive often so I haven't really experimented with it much.
Good advice on using wget or JD, though, I'll keep it in mind for next time.