Apple TV Not Waking on Demand for Computer Behind Switch
I would think that the magic packet is indeed getting "swallowed" by the switch.

I suspect that the UDP broadcast packet containing the WOL magic packet is going through the switch from the ATV while the Mini is switched out. Could you replace it with a hub or router for a time to test? UDP broadcast is always fun.

Can you wake the Mini from the Pro?

If you can then that tells us that WOL is working on the Pro and the problem is indeed the switch. You need to configure the switch so that it somehow holds and rebroadcasts the UDP broadcast packet on all ports.

The problem is that the ATV and Mini are on the same switch.

What is the brand and model of the switch?