Maybe the equipment's terminals are small, loose, undersized.
You can use plyers to squeeze the RCA cable connectors to make them fit tighter.
Or get a super cheap set of cables at Target or somewhere and see if they have the same "loose / too big" problem. They are pretty much a standard size so I can't imagine an RCA being so big or loose that it doesn't connect and loses the audio signal.
I've had a set of cables be slightly loose so they slip off the connectors more easily than normal, and some cables that fit super tight and are tough to get on/off.