Rapidshare can be a pain on numerous levels. Not only is the waiting time a pain for non premium account owners but the downloads speeds can be awful. Also "some" people on certain ISP's get stopped from downloading Rapidshare at certain times in the day. I think it is something to do with Sky forcing you to use their name server, because as soon as you can get the Sky software off of the router you are forced to use and add your own name servers, it works all the time.
The reason stuff gets deleted quickly is due to the Checksum signature (CRC32) of the file. Rapidshare have been on the offensive against people sharing copyrighted material, so they use software that reads the CRC32 and if it detects a file that is the same CRC32 as a piece of copyrighted material that they have previous deleted, the server will automatically block it, even if it is not the same thing as they deleted before.
http://www.fileden.com/ is pretty good as it allows direct links to tracks with no waiting time

Also
Hotfile.com: One click file hosting seems pretty good. Yes there is a waiting time to download, but the download speed you get is pretty good and it also supports download managers.
If you were going to pay for hosting, I would recommend
HostICan - Web Hosting - FREE Domain, PHP5 / MySQL5, Unlimited bandwidth, and more.... As their spring special, they are offering 36 months hosting for $200.16. Obviously the "unlimited" is impossible, but I have never had any issues with their hosting and I have been using them for other projects aside from
SUS for years and I have never been bitten by them. I think I have had 4 hrs downtime in the last 3 years I have been using them