I don't have an HDMI TV but many have reported problems with the cable box and the TVs when using HDMI. My suggestion was to try changing the sequence you use for turn on. Turn on the TV then the cable box or the other way around. My thinking, since digital is all or nothing, it might be like what happens if you connect a DVI screen to a running PC, the screen doesn't wake up until the PC is rebooted when the devices "talk" to each other.
BTW, you might have more consistent performance by using component cables instead.