here could be a broken wire on that side. There are some scenarios of a broken side of headphones that are easier to fix than others. I would suggest simply getting new ones
You will need to figure out which part of the cord where the sound is cutting off, and bend it to get it working again. If you can’t figure that out, bring them to an ERA and purchase a pair of headphones that allow you to use your own line/aux cable. Well worth the money.