If you are running with the top vent open burning coal then I think this is your problem.
When you close (or restrict) the bottom vent (door in your case), then that makes it more difficult for the draw from the chimney to pull air through the grate and fuel, this slowing the burn.
However, if you leave a top door vent open at the same time (often referred to as air wash) the draw from the chimney will pull air in the easy way...through that top vent and not through the door and thus the bed of fuel.
Another thought is you are maybe not putting enough fuel on to last overnight, as you said the fire was empty and cold in the morning?
My lovely old villager heron has a bottom vent the same as yours and stays in overnight easily, even on a small fuel load, coal or wood. It doesn't have a top vent at all!
Finally, wing can have a significant impact on burn rate, so if say it's still when you set the fire for the night, and the wind picks up you can find the room quite hot, but no fuel left in the fire, as the wind increased the draw on the chimney it sucks more air through the same size gap, this increasing the burn rate of the fuel. Reverse also happens, fire goes out after wind drops leaving plenty of unburnt fuel in the grate.
You need to get to know your stove..try different things in the day when you are there and study the effect that changes have.
You'll work it out in the end I'm sure!
Andy