Separate the sides of the zipper by pulling the slider around the frame of the suitcase. Check the zipper to be sure there are no dirt or fiber particles in the coiled plastic strip or individual teeth. Carefully pick at any material that can impede the ease of movement with a sewing needle tip and remove it.
Push any bent or misaligned teeth back into place with the needle.
Close the zipper. Rub the bottom end of an unlit candle along the entire length of the meshed zipper teeth. Make sure the wax from the candle coats the center area of the zipper.
Grasp the zipper pull or slider and slowly unzip the mechanism. Zip the sides closed once again. Add more wax if the zipper has any resistance in the pull.
Spray a zipper lubricant on the enmeshed teeth of the suitcase zipper that is giving a great deal of resistance when the slide is pulled. Try a lubricant manufactured specifically for plastic if the wax is insufficient in helping the mechanism move easily. Follow product directions.