No, you misunderstand. There are many ways to achieve this, but Yummy can do what you want quite simply:
1. Launch Yummy
2. Connect to your server
3. Set up your Sync & Schedule it to run every 12 hours, then click the Run Schedule button
Now the Sync will occur once every 12 hours and if Yummy needs to re-connect to the server it will do so automatically. Obviously the synching will stop if you quit Yummy, so don't do that

If you like, you can option-click on the Desktop to hide Yummy, or just move the FTP Browser window out of the way.
If you do the thing with the connect at startup that I described previously, then you can switch off your Mac at any time, and when you switch it back on, Yummy will start syncing again automatically.