Yeah when you said they've used them for years without issues, that's probably true for their specific shop floor and anvil weight. But even a slight angle or different rubber hardness could make it slide under real force. Solid advice from the OP to check your own setup.
That sliding thing you mentioned sounds pretty wild. I've seen guys use those pads for years without issues, so maybe it's just about the specific setup or how much force you're really putting into a swing. Not sure it's a universal problem everyone needs to panic about.
Remember that time at the forge meet where Dave's stand slid a full foot during a demo? Everyone was SHOOK because his setup looked solid. Just shows how little things can change everything.