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The error you receive may be correct behavior, depending on how your web server is configured via your administrator/web hosting. The default behavior by most web servers is to wait until the first download is completed before serving the same file again to the same browser through the same connection. It may be that your web server immediately timeout during that situation.
I suspect that if you wait for your flash player to complete buffering the media file, the download link would then work as you expect.
I wouldn't put too much thought into this, most podcast downloads occur through the feed via iTunes, other podcasting apps/directories. Your web based podcast traffic will be somewhere between 5-15% of your total media downloads.
If you do end up having a large audience, you're going to have other issues hosting the media files from the same server as your web site. Usually once you reach a critical audience size of about 300+ downloads per episode, your regular web hosting will not be able to handle the serving, bringing your web site to a crawl (slow loading performance). You will need a CDN to host the media at that point. Podcasters either use a podcast hosting service such as the one offered at Blubrry or they roll their own using a service such as Amazon CloudFront.