It may be an IR interference where either the cable box or TV emits a signal that the other device's remote is not working properly with. Some users have tried to put tape (or tape a small piece of paper) over the cable box's IR sensor with mixed results, but I'm not aware of the television emitting an IR signal that should be over-riding the cable remote.

If this continues, you might try a different cable box. If that doesn't work, then you can request a service for your television.