Many loose connections develop where wires are pushed into holes in the back of switches and receptacles and just stick in place. Some receptacles have screw clamps for the holes in back which make the connections more reliable. If not, it is better to use the screws on the sides to hold the wires in place.
When two or three wires want to go under the same screw, cut a short (6" or so) length of wire (pigtail) of the same color and wire nut that to the other wires. Then connect the other end of the pigtail to the screw. The exception is if the wires, if not curled around the screw, are held in place by grooves or a retaining washer as opposed to just the tightness of the screw.
After removing the wires from the push in holes, you may notice the wire end nicked. If so, snip off the end and cut back the insulation to get a new bare wire end.