If a user has clicked the "Do not prompt me again" option in the "Save Results" dialog box, is there a way to bring that back to give the user the option again?
Sure. Go to options Environment | Confirmations. Press the "Reinstate all confirmations" button. That resets everything. If you want to only get the one confirmation back, you can look in the footer of the app. When it would normally be displayed, you can see the message written in the footer with an "enable" link. Pressing that will enable just the one message.