I had the same problem. Requiring users to modify their clicking habits seems excessively onerous -- especially to "prove you're not a bot." The fact that you had to explain to me why a bloody web button didn't work proves the point; it's like throwing out the baby w/ the bathwater.
It's a trick I learned from industrial SCADAs. Sometimes buttons simulate how a literal contractor works by watching for down-debounce-up events. No idea if that's the case here, but it seems to help to dwell slightly on the button to let the event thing really catch the event fer sure.