this car sits a lot: in summer it gets used on weekends but in the colder months it may be a week or two between starts. I recently had a new battery installed and a week or two later (with frigid temps) it was dead again. AAA came and jumped it and the battery tested okay (clue #1, I believe). That was last week and again today (more frigid temps) it was completely dead. Now, by "completely dead", I meant the remote will not unlock the doors and turning the ignition results in complete silence. No sooner do I get the jumper cables on the alarm starts beeping and it starts up. I noticed the clock showed 1:00, while it was actually about 12:15 (clue #2?). So I let it run a minute or two and put it in drive and every warning light on the dash came on, while the radio started intermittently went on and off. Even the speedometer was acting erratic. This went on for half a mile or so and then everything was fine, including the clock accurately showing 12:27, and my radio presets all just fine.

Does this tell me anything about my battery cables or ground? I mean, it couldn't have actually been 100% dead if the clock and radio presets came back, right?

You need to take it to an auto store who can provide an analysis of your battery and charging system. A new battery should last you a few years, if it is losing the juice quickly, there is something going on. Take it to an auto store or to your favorite shop who can provide a free analysis.

Were the battery clamps and terminals cleaned when the new battery was installed? That's an easy thing to check first before looking for something more serious.

No, no, no. You have parasitic drain. It kills your battery fast. You need to find a guy with multimeter and scope, what does this.

One area to check is the lamps in the rear cargo area, They have a on and off switch. Under the sliding cover you may not notice that they are on with the car shut. Just a quick check. After that it could be parasitic drain on battery....Please note there is always some, it will never go completely away. You could use a meter with amp settings and hook meter between negative lead on battery and cable (disconnected)….Leave hood up and after 30 minutes see how much drain in amps is happening after turning car off. It should be very small. If the meter reads 1 to 2 amps, that will drain battery fast.

"clue #1" was that AAA tested the battery after the first jump: it came back 100%.

​​​​​​​If it's parasitic drain, how do we account for the fact that the clock comes back on the correct time (after a minute or so) and the radio presets are preserved?

It's at the garage that insalled the AAA battery; I'm hoping they'll figure it out.

Because battery still has residual power enough for low draw devices? There is huge difference between maintaining clock and radio memory and starting engine.

I would have thought it was bad battery, but since you have the same issue after swapping out for a new battery, I would assume that it's a parasitic drain (from an aftermarket accessory) or you swapped in a bum battery.

If you bought your RX new and didn't add any aftermaket or modifications, it's totally possible that the new battery is defective, especially if it has been sitting around for a few years. Have you checked the electrolyte levels in the new battery?

I had new batteries swapped in about 4 years ago by the Lexus dearlership and within a few years, I had the same issue that you had. I checked the electrolyte level and the battery was practically bone dry. Top it off with new electrolyte fluids ($5-8 at most auto parts store) and have had no issues since.