I've seen this posted before, but I don't recall what the outcome was. You might call the cable company up to see if there's a reset or an update to address this issue (since the box is freaking out, and not the television, it likely points to a box issue).
You certainly shouldn't have to unplug the cable every time you turn off the TV, but if the update or reset doesn't work, you may want to see if they can switch out your box.
I don't think it's the television, but I have no way of definitively assuring you of that - but that's what I'd do.
I have a Samsung LN37A550 37-Inch 1080p TV and Scientific Atlanta TW cable box. I'm connected using HDMI and every time I turn the TV off the cable box goes into a "boot" phase after about a minute.
If I remove the HDMI cable and leave it unplugged then the cable box corrects itself or I can remove power from the cable box and let it go through the "re-boot" process which takes several minutes.
The solution I've found is to unplug the HDMI cable every time I turn the TV off.
Has anyone found a solution to this problem?