How can I set up a change of state so that a button retains the down state once clicked

The Down state is one of the InBuilt states. It is not a normal behavior of a button to remain in that state when the button is released, but here is a work flow to realize what you want:

• Open the Object States panel
• Duplicate the Down state, it will be a custom state that you can give a name, I'll name it 'Done'
• You'll have to create at least a standard action for the Success event of that button, you don't tell which action is triggered at this moment, but you'll need an extra command:
  • Change State of Button to Done
  • your action

If you want the button to keep that state, even after leaving the slide and returning, you have to check that option in the Properties.