Updated 05/25/2011: Save yourself time, money, and frustration by checking out my latest solution.
Well, something seems to have worked. I’m down to three possibilities.
(1) Batteries were low
(2) HDMI to Ethernet Extenders were causing interference
(3) Antenna connection was loose.
I think I can rule out #3 since it still seems to be responding better than it has for a while. If it was the antenna connection then I would have seen the reliability change from time to time. I don’t think it was #1 because I had previously swapped out the batteries though I went ahead and changed them again just in case I happened to have a bad set on the last change. The other, and perhaps more likely possibility, is that the HDMI to ethernet extenders were causing RF interference. Since the extenders were sitting up next to the antenna this would have been a problem if they did generate RF interference. To eliminate this possibility I swapped out the short HDMI cable going from the extender to the DVR with a six foot HDMI cable.
At the moment it seems to be working fine. Of course, it may not after I’ve published this update.