Thanks for elaborating on the requirement.
Our server product, CompleteFTP, would be able to do what you're describing through what we call Process Triggers. These can be triggered by a timer (i.e. scheduled) or by an upload, which sounds like what you need. However, since you already have a server, this would require you to replace your current server with ours.
If replacing your current server isn't an option then I guess you're looking for SFTP client software to integrate with your existing SFTP server. We have two client products, edtFTPnet/PRO and edtFTPj/PRO. Both of these are primarily libraries for use by software developers - the former for .NET, the latter for Java. A secondary feature of both of these products is what we call a scripting engine, which allow you to execute SFTP scripting commands from the command-line. So you would be able to use either of these two products, either to developer your own .NET or Java program that would perform your SFTP functions, or to execute simple SFTP scripts that are called by cron (on *NIX) or the Windows scheduler.
I hope that helps with your decision making.