Sounds like some kind of hand-shaking issue with the cable-box. You can try another HDMI input, though this will really only tell you that the problem is universal, and won't really pinpoint the specific device having the issue. The best thing you can do is just call the cable company and have them send you a new box. The box belongs to them and unless you change the TYPE of box, they should not charge you anything for a swap out.
I mean, you could hook an Apple TV or something as well but you'd have to watch it for hours, days or weeks to see if it happens there as well.