You can download if you connect to the camera directly, instead of through the mydlink.com website.
If your computer is connected to the same router, put the camera's IP address in the address bar of your browser. You can find this address in any of the motion detection emails your camera sends (look for 4 numbers separated by periods, for example 192.168.1.2; this address might change occasionally like after your camera disconnects then reconnects), or your router may be able to tell you (where to find that depends on your router). If you're not local it's a bit more difficult but you can also do it. In that case, look for the 8 digit number under your camera's name on the tab on the left of the mydlink camera view. Take that number and put it in place of the www in the URL. For example, https://12345678.mydlink.com, click OK when it tells you to not leave the page, and accept some other warnings.
With either of these methods, you'll arrive at a password prompt. Put in your camera's userid (probably admin, and whatever admin password you use). Then click Setup at the top, and then SD Management at the left. Then click on a date, then an hour, then a file name. Then at the popup click save. That's it.