Without updating the firmware, have you tried running the DAP-1360 as a AP (installing it temporarily), in a good spot and running a standard CAT5 TP-cable.
Just to see if that works fine, if so, they you know that using the DAP-1360 as a repeater does not work well for you. Then if possible you could figure out some permanent installation of the DAP-1360 running as a AP instead of a repeater.
Upgrading firmware is a good thing, but make sure you have the correct firmware, otherwise you could brick the unit. Or run into other problems.