I can't download replays given to me through the forums and most likely skype as well. I don't know what I've done, I just can't download anymore. I did download the non-steam version, maybe that could help. I will most likely have more info soon to help fix it.

are you using google chrome ? if yes just right klick on the replay and open link in new page (worked to me)

check if your firewall or antivirus is blocking downloads

same problem here.

the problem in general is that the forums have been awfully slow for me at times lately. every other website works fine.

Try using a different browser, but I'm not sure how your skype is unable to.
For skype, the person muse set their status to "Online".... that's the only thing I can think of.

Are you using Windows 8?
If so, then I think there's an option for downloads somewhere.

Try another browser, i had this problem too and when i changed the browser it worked fine.

Tried all, none worked. I am on windows 7. It probably had to do something when I once had the steam and non-steam version at once.

Try to use different Website, I remember that happened to me once but, I couldn't Upload, Check your downloads (If yo using google chrome) or maybe you have fire wall or something like AntiVirus that doesn't allow you to.

Did not fiddle with antivirus or anything. Tried another browser as well.