Instead of describing what's happening I'll post a screenshot of Apache's server-status page:
It is a Nigerian IP.
I'm having this problem for years now and I never found a viable solution except banning the attacker's IP and waiting for the jerk to return via another one.
Here's a bit of further explanation. The site is custom developed and that download page is only accessible if the user is logged into the site, otherwise a redirection to the login page is served. If the user's logged it serves quite a big file. But, after serving it once, the site has sort of a RapidShare like politic, meaning that the user has to wait. So the second time it is accessed it'll only serve an error message telling the user to wait. However it looks like the attacker somehow succeeds in opening a connection and then another one and then yet another one, until MySQL on my server chokes up and starts throwing errors.
If this kind of attack is a known one, has a name and there are known solutions on how to avoid it redirect me. Any feedback or ideas are very welcome because I'm slowly going crazy here.