I'm just re-read this entire thread, looking for anything I missed and just generally trying to get a clear picture of this difficult situation. I still don't have a clear picture, so I'm hoping you might compose 1 good message to summarize all the available info. Hopefully that can give us a fresh start that leads to ultimately figuring out why you boards are failing.
I see you shared a photo of the PCB in
msg #8 and a schematic in
msg #17, and answered followup questions on the VR1 part. While better than no info, I want you to understand this still doesn't give a complete enough picture. In particular, the schematic shows 3 connectors. One is to a display, which seems unlikely to be the issue. But the other 2 connect to stuff we can't see. I should also mention your photo has 4 connectors visible, not 3. If Teensy is dying from some issue with the connected circuitry, everything you connect is effectively part of the design whether it's part of the schematic or not. I understand this is probably a commercial product where you're not eager to share all details, but in the interest of helping you look for anything that might be damaging your boards, the more clearly and fully you can show us everything which connects, the better the odds are someone here might notice an issue.
But the ultimate problem might not be your PCB and other circuitry. Very difficult to know. Of all the messages you've written so far, these words in
msg #16 really stand out (to my eyes)
My best guess about a situation where a previously thought-to-be-dead USB powered board starts working again, but only briefly, may be a problem with USB power delivery.
@PaulS already asked several questions about your USB power, but I want to also echo that concern and emphasize further investigation with some specific tips...
Start by monitoring the USB voltage and current. There are many ways you might do this. If you don't have traditional gear like a scope or good multimeter, at the very least please use an inexpensive device like one of these so you can see the actual (approximate) voltage and current at all times:
USB hosts and hubs are supposed to implement over-current detection. But how specifcally they do this and how they recover from a fault condition isn't required by the USB spec. Even for things the USB specs require, how well implemented they are in any specific hardware varies quite a lot.
Some USB hosts and hubs will temporarily disable a USB port if the connected USB device misbehaves, especially related to drawing too much current. They may detect a problem quickly, or it may take time, which could be a limitation of the hardware or an intentional design decision to allow some types of USB devices to work. One possible theory (or guess) about what's happening could be the USB port on your Mac might be silently shutting itself off.
That's why I'm urging you to connect a voltmeter and ampmeter, or at the very least get a couple of those cheap monitoring products which do it, so you can keep an eye on the voltage and current at all times while trying to diagnose this problem.
You might also try connecting with a couple different powered USB hub. Don't use an unpowered hub... but one (or 2 or 3 for the sake of testing) with power supplies, so the hub provides the power rather than your Mac's USB port. The hub takes over the job of detecting too much current flow, and of recognizing when a USB device is connected and unplugged.
If you're going to make a PCB rev, I'd also highly recommend adding a connector or
test points to monitor the 5V input and Teensy's 3.3V power. Or for the PCBs you've already made, just solder some wires. If you don't already have a couple voltmeters, buying even the cheapest models can give you a way to always watch the 5V USB and 3.3V from Teensy. Like monitoring the USB current, while you're troubleshooting I would recommend always having those visible. Maybe nothing anomoluous will appear, but if you do see them change in any unexpected way, that extra info and seeing it happen when you try specific things could be the clue that leads to a breaktrhough in understanding this problem.
But again, this is a lot of guesswork from only a very small number of words and a rather incomplete picture of the hardware really connected to Teensy. I know you're probably not wanting to share so much detail, but if you could better show us ALL of the stuff that's connected (not just the PCB but anywhere an electron could go) maybe one of us might notice something that's been so far overlooked.