No battery power

If you have an auto reset circuit breaker in the battery positive line, that would definitely be a suspect. They are very cheaply made and known to fail.

What they said allready, check the battery for power then follow the line. There will be an inline fuse or autoresetting fuse (they do go bad). Check to see if power is getting through that. Put a multi meter on your inside fuse, sometimes they look good but aren't. Clean up the ground conections.

Without digging into it yet, my guess is that there is indeed corrosion in there. Our in-line fuse is supposed to have a cover on it, but that was connected by a little rubber cover which has been gone for years. So when I pull the fuse in between trips, that fuse “box” is exposed to the elements. I’m assuming I can find a replacement fuse box to upgrade that and splice it in?

On 12 volt systems the ground is the most frequent issue, not just at the battery connection, but the other end of that cable and where it attaches to the trailer chassis. A quick check is to use a jumper cable from Battery neg to the metal at the hitch. 10 second check, and eliminates half the possibilities.

Follow the positive cable lead from the battery. I believe you will find a circuit breaker that has failed. It is normally located at the junction of the battery, rig's wiring system and the umbilical cord from TV.

I had the same perplexing issue a couple of TTs ago. Exactly as you describe.
After pulling what's left of my hair out trying to figure it out, I decided to follow the 12V positive wire. I probed it at the hitch where it went under and into the TT. Power there, but nothing inside at the converter fuse panel.

I got on my back and slid under the front, behind the frame cross member where the wiring went in.

I shone a flashlight up to the bottom of the floor, right behind the front frame and discovered a cluster of connections hidden in there. One of them was an inline fuse for +12V. I opened the fuse holder and Bingo! There it was. The fuse was not blown, but the holder and ends of the barrel fuse were corroded, just enough to make the connection intermittent.
I cleaned up the connections, put it back together and voila! End of problem.
It never happened again.

With any luck, perhaps you can find a similar issue.
Try tracing your +12V feed from the batteries all the way back to the converter.

When plugged into shore power, the 12V comes from the converter, regardless of whether the battery works or not.

BB_TX wrote:
Did you by chance turn your battery disconnect switch?

Good thought, but we don’t have a battery disconnect switch. We physically pull the fuse, and the fuse is still good.

Did you by chance turn your battery disconnect switch?

Sounds like a bad ground or possible positive power block issue. Check where the wires coming off the battery go

Intermittent issue is generally a loose connection or bad/loose or corroded ground.
Where to start? Both ends of the big cables from battery to converter.