Because the addon is LOD, its frame is created after the PLAYER_LOGIN event which means
SetUserPlaced doesn't work (save/restore the last known position).
You will need to save/restore it's position manually or you could try creating your drag frame when your addon loads (ie. use your EventFrame (and give it a name) for the drag frame and set it as dragable, user placed, OnDragSart/Stop etc.) and when the AzeriteEssenceUI is loaded, resize it to the width of the AzeriteEssenceUIx15 and Clear/SetPoint the AzeriteEssenceUI to your EventFrame.