Congrats on your new Heatmor.
The restrictor is basically just a washer welded onto the end of a tube to limit the amount of air blown into the furnace under the grates. The manual says if your going to burn coal, you need to remove the restrictor.
As far as keeping your fire from burning out, it could be a few things. If you just started burning, you may not have a deep enough bed of embers for the type of wood you are burning. Some wood types smolder better than others, so if you have say poplar in there and you don't have a good bed of coals/embers, the wood will just quit burning during long smolder cycles. If you've been burning a while, you may have too much ash built up and that could be limiting the amount of air getting into the firebox. I find if I've blown off taking ashes out for too many weeks I have a hard time getting the stove up to temp.
Hope you enjoy your new machine as much as I have. I still find myself standing outside watching it work and think about what a great investment its been.
Steve