Usually unburnt coal in the ashes is a problem with the coal. Substandard coal has a lot of black shale [rock] in it that looks like coal, but won't burn... also a lot of coal breakers are using 'reclaimed' coal for their rice and buckwheat size coal they sell.
This 'reclaimed coal' is the coal stacked up in huge piles around the breakers that has sat there for decades.. The piles are of small size coal.. it was the leftovers from breaking up large coal down to stove, nut and pea size. Untill recently there wasn't that much of a demand for smaller sizes like rice.. So the piles sat in the sun, wind and rain for decades.
When coal sits in the sun, wind and rain, some or all of the 'volitiles' evaporate away, this leaves some of the coal VERY difficult to burn.. Some just won't burn..
So the unburnt in your ashpan may be just bad coal..
OR: is there a dark spot on your burner?? like a pie shaped wedge that is dark, where the coal is not burning??
Are you pulling the lever every day and dumping the fines into the ashpan??
If you have a dark spot, you have a bad grate-section, you need to shut it down, clean it out and replace/reseat/reseal the grate, and clean out the fines.
Take a look at the burn pot, is there a even red/orange ring of hot coals, with an even perimeter of ash?? Or is it irregular, and a part of the hot coals dropping off the edge into the ashpan??
Hope this helps,, give us some more info. maybe we can helps.