http://community.cambiumnetworks.com/t5/ePMP-Installation/ePMP-Powering-at-Sub-freezing-Temperatures/m-p/48918/highlight/true#M27
Even if you're not in a cold region, i suggest you double check your cable connectors(for correct crimping), and make the cable runs as short as possible, both in the ethernet and the DC cabling system.
Avoid as much as possible connectors in the DC powering side (barrel connector, etc).
When under discharge, your battery bank will go as low as 10.5v, 7w/10.5 makes for 666mA.
That's some considerable current given you don't have many spare volts to drop.
it should work if done carefully, good luck!!