First you don't have to buy it again. The app's license is connected to your Google account/mail address.
Before you run a firmware update you should first uninstall the rSAP system files, either with the installer app or the rsap-uninstall.zip. Else it may happen that the update fails. As far as I know the 4.0 -> 4.1 update is done in KIES, this may work without uninstall, but I'm not sure.
After the firmware update the rSAP system files must be reinstalled. If your phone was rooted before the update it is no longer rooted after. But before you install anything you may give the Samsung rSAP a try. If this doesn't work you can still reinstall my app