Sansa Fuze died, won't power up

Yes, the 20 second hold is a reset. If you have your headphones plugged in you’ll hear a little click some seconds after it goes dark.

Why?

It can happen if you disconnect the USB from the computer rather than the connector from the Fuze.

It can also happen if you don’t Safely Remove Hardware and disconnect while the Fuze is still talking to your computer, or if it’s disconnected when something hasn’t finished transferring, or if there’s a file the Fuze can’t quite handle.

Or the Fuze could just be having a diva moment.  That’s why there’s the reset.

And yes, I suspect the other two were the same. But I hope you got a warranty replacement.