Not an electrical engineer, but I was 2 sentences in when I declared to myself "its the external clock source" and then a physical shudder as I remembered how many times a contract manufacturer has used some aging crystal or third party component src and not updated the matching capacitors, causing very similar issues on projects I've worked on in the past. The very very worst is the aging xtals - a warm wind can make them work for an undetermined amount of time, which is bad if the factory is running warm around 26C or so and you end up shipping the batch to Europe where its early winter...

I wonder if the author is right; using a slightly wrong capacitor for the clock (keeping in mind that they're usually +/- 10% or worse from the factory) may produce a different oscillation speed, but usually not an outright failure. These chips accept a pretty wide range of clock frequencies.

And in the comments, they note:

"I replaced the 18pF capacitors on one of the non-working boards with 10pF capacitors, but it still doesn’t boot or respond to the debugger. That surprised me – I thought that was the answer! It was a rush rework job and I made a bit of a mess of it, including accidentally desoldering and reinstalling the crystal, so I’ll try again later with another board. But it appears that the capacitor value may not have been the issue after all. Either 10pF is a bad value, or it’s the crystal itself that’s at fault, or I’ve failed somewhere in my troubleshooting reasoning. Hmm."

In my experience, mystery stability problems are often caused by capacitors, but of a different kind: decoupling capacitors on the power supply pins. If there's not enough of them to keep up with the noise originating from motors or digital switching, I'd expect that exact issue. Intermittent "impossible" CPU states on some boards, no rhyme or reason (because sometimes, that +/- 10% saves you and sometimes it does not). I'd try more caps and possibly some ferrite beads.

When I got to my current workplace I was surprised to see we always, invariably (unless it's really impossible with the chip) use an oscillator not a crystal. But every time I see one of these posts I think about the difference in cost for us relative to the math of capacitance and debugging, it's just not worth it. And of course the first board I worked that we basically built to print and had a crystal integral to the design... They got the capacitance wrong and it didn't go.