Hi, thank you for contacting JustAnswer.com. My name is Russell. I will do my best to provide the right answer to your question.
Your Garmin Approach may need updating with Garmin Express. Not being able to save a golf score may be a symptom of such a need for an update... not a periodic update, but perhaps a remedial update.
Or, you may not have specified a location or name for the score first, or the like.
That is done by connecting the Approach to a computer running the Garmin Express program, basically.
When connected to the computer, you could also transfer scores to the computer.