Something discontinuous does not run in a smooth, unbroken line. It has gaps. Discontinuous sleep means you keep waking; a discontinuous journey has stops and breaks; in maths, a discontinuous function jumps or has holes. The everyday opposite is continuous — going on without a break. Teachers and scientists use it more than casual speakers, who might just say on and off or with gaps. It describes the shape of a thing or a process, not a company’s decision to stop selling something.