Powering EL Wire from a PoE power source
Very likely, the PoE injector has a current limit circuit to deal with a cable or device fault. For example, this Wikipedia article claims 350mA / 600mA limits for 802.3af and 802.3at  Moreover, it seems that the limits are negotiated, so you could be set to an even lower limit.

The limiter would be there to protect the power supply and to ensure the continued operation of other devices that are powered by the same injector.  And, more importantly, to protect against unsafe short circuit currents in the cabling which could, in the extreme, lead to a fire.