It shouldn't matter what your downlod speed is. The problem is likely due to one of the two connections having packet loss or losing the connection. Try pinging the target and see if there are any lost steps. Also try a tracert.
Open a Command Prompt
Type: ping "website_url_here"
Type: tracert "website_url_here"
As mentioned, just post the results here. If you think it may be something to do with Windows or the browser's download manager you could try a different one.
FlashGet works really well and actually speeds up your downloads.
If you use Firefox
you can use the same that I do:
The FlashGot extension
in conjunction with FlashGet 1.9