While it is possible that the Last few troops on each side will be able to run it down to a stalemate, is that really a problem, or a feature?
In order to get a stalemate, both sides will have to be very short on firepower indeed. I don't see that as being to unrealistic.
Aside from that, once combat has progressed to that stage, all you need to do is drop a handful of reinforcements. A single transport would be way more than enough.