Chosen Solution
When on battery alone, the computer signals low on charge and turns off when the charge, as shown by the menu bar at the top right of the screen when I plug the computer back in, is still 85%.
Try using Coconut Battery to see if the issue has to do with the health of your battery. Another way to do this is to go to System Profiler and go to Power and under that it should say if your battery needs to be serviced. Usually in this case, the battery is too old and it won’t hold a significant charge anymore.