Passive mode is something you configure in the ftp client. It will let you use ports other than 21, and is intended to let you transfer files while sitting behind the protection of a firewall. Passive mode can be disabled through an ftp server, which may be why your friend had problems. Dreamhost supports it though, and I always connect with passive mode.
You're experiencing this in a real ftp client, and not just using the ftp capabilities of IE, right? Is there anything consistent about the failed downloads? Such as particularly large files, or files that the webserver may be asked to serve up while you're downloading?
Make sure your ftp client supports resuming, and enable it. The Dreamhost servers allow this, and you'll be able to continue your download where it failed the first time.