I now doubt the finickiness is due to play in the thread. Comparing with an Olight I3E, the C01S has much finer threads and less play, yet the I3E has no such issues.
My latest hypothesis is it might be due to the contact patch design. Notice how the C01S has less than half of the circumference of the PCB metalized for contact with the tube’s negative contact. The I3E has nearly the entire circumference available for contact.

The I3E’s tube (negative contact) has a pretty flat contact edge, while the C01S’s tube has a beveled interior edge.

In particular notice the kink at point A showing an enlarged bevel. I suspect that the head’s contact protrusions have been acting as a drill bit starting around point B until stopping at point A where the difference is most pronounced. There is a similar pattern 180 degrees away. This means the contact is at an angle and has now become more distant before making full contact. This might explain why I now need to screw the head in fully for the light to turn on solidly, compared to when it was brand new (not even a month ago).
Notice how the C01S’s head contact area is protruding like a drill bit. The metal is uneven and has either worn off at the very edges or was not fully coated. Wear marks show contact is made near the edge, which might explain flakiness.

Overall, I’ve been happy with the twisty style of operation, but the C01S’s implementation leaves something to be desired and gives me concern for future reliability.
I’m not certain of this diagnosis, but surely the following recommendations wouldn’t hurt:
- no beveling inside the tube, only deburring, to allow larger and flatter contact area
- metalize the head’s negative contact all the way to the edge
- increase fraction of the circumference that is metalized
- consider a circular PCB instead of one with protrusions which can act as a drill bit
The last point might not be possible with the current implementation since based on the wear marks, the contact seems to be made just at the border of the diameter of the PCB without the protrusions. Maybe that is why the protrusions are there in the first place…