I've done a bit more investigation into this and people have said that this can be fixed by forcing curl (which Dropzone uses) to use HTTP 1.1. I think it's caused by some specific network configuration as another customer emailed me to say he was having this same issue and after he swapped out his router the issue went away.
I've made the change to force HTTP 1.1 and this will go out with Dropzone 4.0.9. I'm pretty optimistic this will resolve it. I'm in the middle of some other major development on the app though so it may be about a month before this update goes out. But try it again when 4.0.9 goes out and hopefully that will fix it.