I cable-tied the mic/earphone cable on Mary’s bike helmet to a rib on the fancy air vents near the back end, hoping that would reduce the inevitable flexing. Alas, it didn’t work out that way and the cable lasted only two seasons. This cut-away view shows the pulverized shield braid inside the jacket:
The symptoms were totally baffling: the mic worked perfectly, but the earphones cut out for at most a few syllables. Of course, I can’t wear her helmet and it only failed occasionally while riding. I barked up several wrong trees, until it got so bad that I could make it fail in the garage while listening to the local NWS weather radio station.
I spliced in a new USB male-A connector and (re-)discovered that the braid seems to be aluminum, rather than tinned copper. In any event, the wire is completely unsolderable; I crimped the braid from the new connector to a clean section of the old braid. The braid serves only as an electrostatic shield, as it’s not connected to anything on the helmet end. That should suffice until I rebuild the headsets this winter.