Are you 'right-clicking' and hitting 'save as' on the local links? You want to left-click once, and the download will start automatically. It will give you a pop-up to either play it or download it - download it to a folder on your comp. If you have any download accelerators installed, disable them (things like DAP).
If you *are* left-clicking the green local button, then cancel the box that pops up and wait a minute (some 60 seconds) till a link appears. Try downloading that (again, just left-click it, don't right-click it, and don't try to use a download accelerator).
You might also try clearing your cookies if you're using Internet Explorer. Log out of your account and close the page. Right-click your Internet Explorer Icon and go to properties. Click 'delete cookies,' click 'delete files,' click 'settings' and 'view files' and manually delete any cookies that remain. Open a new page and log back in - retry a local download.
If none of that helps, then you want to take the quick and easy way around the problem (instead of fixing it) and download a different browers. Opera works good -
www.opera.com since it lets you resume local downloads.
All of this assumes that you've been a member for 2 weeks and you haven't defaulted on any pledges.