I would try getting the latest firmware for the small business switch. This could easily be a firmware issue. I think this is the most likely issue. Perhaps the switch is crashing rather than powering down.
My next guess, which I think is unlikely, is some kind of PoE mis-negotiation is happening, and both ends are trying to apply power (and causing a short, or something like that). Perhaps see if you can disable PoE on the port on both ends.
I'm assuming you have tried a different patch lead already?