No, your files are not removed from our servers after you have downloaded the restore.
The message Once you download the requested restore, it is no longer available is a warning message stating that the specific archived restore files will no longer be available for you to download. You will have to perform another web restore should you need to download those files again.
Note: If you are replacing a machine on the account, the files backed up from that machine will only be available for 30 days after it is replaced. It is recommended you restore the files before replacing the system.