Thanks, everyone, for the input.
@MrPogi, I have rescanned the channels to no avail. I get the same 19 channels (which I realize isn't bad with an antenna) but 51.2 won't show up.
@ATL Royals, unfortunately I don't know the make and model of the DirecTV antenna. It's something they sold me for $50 probably 10 or 12 years ago when they weren't offering local channels in the market (in the analog days). It's high atop my two-story townhouse, so it's not like I can access it. I also live on top of a hill with clear sight lines, so the PQ I get is outstanding on the channels I get. No splitters or squirrels that I'm aware of.
@Jim, the rabbit ears are on a different TV set. The off-air channels show up on my DirecTV grid guide (I've kept an older receiver for that purpose), and I have rescanned the locals several times over the past couple of years.