Hmmm. So what else changed about 3 weeks ago? You've probably already addressed these items -- I don't mean to insult, I'm just trying to help -- so just in case:
1. Has your internet DL speed changed, or have you only noticed the problem for rapidshare?
2. Does the same thing happen with megaupload or other file hosters?
3. Is your hard drive within 5-10% of its capacity? I've noticed that when I get close to maximum, my download speeds drop off (which makes sense as everything else slows down too).
4. Do you use special software/progs to download, and could that be an issue?
5. Free downloading, or do you have a membership? If you're a member, have you tried downloading as a free letters-with-cat-identifying downloader?
6. Have you tried bouncing around between different DL servers? Usually when you download RS sets your DL server to some default, probably whichever one is the least utilized on their end. Sometimes, when I get some sort of silly slow download speed, I cancel, redo, and try a different server from the default, e.g. cogent, teliasanora, whatever, and all is well.
As an aside, there are certain times when RS is much busier than normal, like on ... weekends, when people from all continents access more at all times of the day.
Anyway, other than the above, not sure what else to say. There are other (far) more technically gifted helpful people around here, so if none of this helps maybe you could provide a little more info and see what happens?
Anyway I hope it gets better for you, slow speeds like that are horribly frustrating.

When I was living in India I was lucky if my ISP was giving me 256K connectivity, so I can relate!
RM