@Jumpluff - It shouldn't make a difference between Save/Open. When you "open" a file, it saves it in your temp directory so it's still on your harddrive and opens it. It deletes it when it is done with the file, whereas save, you keep the file when done.
Yes, I know -- if he's having problem saving it, the fact it's saving but in the temporary directory, then deleting afterwards, could be the issue.
D-Rat, what browser are you using? Safari? Which version?
ETA: Alright, since you are using OS X, I will assume you are using Safari; correct me if I'm wrong. If no prompt is appearing when you click Download on other sites, open Safari Preferences (I think it's in the Safari menu heading), go to General, make sure a location is set for your Downloads folder, etc. If it seems unique to Shoddy Battle's site, let us know.