No such luck so far, but I'm still looking, going through my home and trying to apply everyone's impressions.
Re: heating/air ducts, well, I have some odd heat units in my apartment. My dog, ahem, messed one up last year, so that the vent portion is partially exposed. I caught myself looking through it to see if my remote could've fallen in.
Re: outside/under something round or dome shaped/near water: First thing that came to mind was the little recess in my kitchen where the water heater is kept, because this is where I store my garbage before hauling it to the dumpster, and it has occurred to me that I might've been not paying attention and thrown the remote away while picking it up along side real garbage.
Re: mischief. No children, but I do have a dog, though he's not generally in the habit of stealing things that aren't already cleared for him as toys, or food he hasn't been told to leave alone.
Re: kitchen area. The black surface would be my cheap folding table. I spend a great deal of my time in the kitchen, using the table as a computer desk and also taking my meals here. Only white surface would be my stove. Caught myself looking around and behind it, esp. with the above mention of dust bunnies.
Have to say, I'm still new enough to all this that I'm fairly amazed at what people are seeing. When I would get up from watching t.v., the remote nearly always traveled with me into the kitchen and ended up on a table (I have two tables in the kitchen, the aforementioned folding one, and the *actual* kitchen table, which doesn't get used for much more than storage), which is also where a lot of my trash accumulates before actually getting tossed. All these things were on my mind as I typed my post last night: mulling over the possibility that I long ago accidentally threw it out, or took it outside and dropped it, or that it ended up on the floor near or behind the water heater---I even found myself side-eying my dog and wondering if he'd taken it upon himself to bury it. Could dwelling on those possibilities have interfered with people's attempts to "see" it?
Anyway, I appreciate everyone's help. I'm going to go back through everything now and see if I can come up with something I haven't checked yet based on what's been suggested.