I thought I'd post this problem and its resolution here in case anybody else encounters it.
I was configuring an OmniTIK UPA-5HnD with a single outboard SXT as a feed link. I couldn't get the SXT to power up unless I forced the port's POE-out on.
The problem turned out to be that the cable I had inserted into a spare port for a debugging connection happened to provide POE in. It looks like if you supply POE-in power to any port other than the first port, it screws up the auto-sensing of the POE-out circuitry. When I removed the power injector on that cable, the SXT port immediately lit up.