NY formulated on Saturday :
I can imagine that sweat on the metal terminals *may* cause a bit of
oxidation over a long period of time, but I can't see how a body resistance
of many kilohms will cause the battery to go flat.

It's the sweaty/oily deposits from your skin which is a problem, it can
short across the insulator and cause the low power cells to discharge
and reduce their working life. You should only touch them with
insulated tweezers, to avoid this.