The eDP connector is internal, presumably not connected to anything, and I assume that your display is connected to one of the external ports, so that is why your display goes to sleep.
You should leave eDP disabled.
eDP is internally connected to our custom hdmi add on board.
Oh, OK. Does that mean that you have a single display connected to your custom HDMI add on board? Or do you have two or three displays connected?
Can you please send any document describing the real world scenario using eDP on NUC.
Sorry, but I can't help you there. Maybe someone with Intel...
Intel provides with additional headers on the NUC kits for custom builds. The Intel® NUC Kit 5i5MYHE is a vPRO unit. They are intended for business purposes, the unit gives the opportunity to create your own chassis and add more hardware to your system.
This NUC has an internal USB2.0 header, eDP, Header with PCIe x4 and internal 2x2 power connector.
Technical Product Specification 5i5MYBE