Almost all of the time, if you are downloading something from someone, any problems are caused by the sender and not by you. That said, you might have intermittent internet problems that are minor enough to not be seen anywhere else, but still enough to cause a DCC download to fail. DCC sends are much more sensitive to poor internet connections than many other common transfer methods.
As far as resuming a download, not everyone has the ability to resume sends. If it goes right to 0 without doing anything, then the sender cannot resume a download. It is possible they could make a change that would fix that, but that would be something they would have to change. There won't be anything you can do about it other than to let the sender know.
Remember that DCC is far from the best method to download things. There are many better ways to download stuff. If you have trouble with DCC, just choose a better method.