It turned out that the problem was a ~60V potential
difference between the
grounds on the outlets we had the two soldering irons plugged into in two
spots on the bench. As soon as someone tried to pick up something with
both irons (e.g., an SMD resistor), you put a 60V potential across whatever
part of the board you were working on. The buffer amps did NOT like that.
We figured out the problem when we noticed that LEDs were lighting up when
we picked them up with two irons.
How do you end up with 6V between the earth pins of 2 sockets on the same
bench? If I could measure any voltage at all, I would want to know the
reason why.
-tony