I have crossed the bridge a number of times. You’re having trouble with your USB charger. If you get the message “Not charging”, it’s NOT CHARGING. Once the battery hits zero, you’re out of luck unless you have an effective charger. You might try buying a new one from Microsoft, any USB charger won’t do. I’ve had luck with the Anker batteries with quick charge, they can charge your Surface 3 and double your battery life on the road.
I have been with this problem before. You may like Robert M. said, get a new charger. But my friend told me to buy some rubbing alcohol and dip a Q-tip in the rubbing alcohol and put it in the slot where the charger goes, as well as the part that goes in the charger.