There is always an solution
Real inspirating game concept - I like it a lot.
Besides fo more levels, there is not much to improve - maybe I would have liked some changing music or so... your one got boring after 10-20 rounds ^^
To Ice-Mage545 Problem:
There is always an solution. Sometimes you have to provoke them to move so they don't shield each other anymore, as it is normal in chess to do so. Try another position for an "attack". If you stand on the right field one of them WILL move, even if it was formerly already "attacked" from a different field and didn't move. It really depends on the field youself stand on - believe me.
But the stones, you are right, don't ever react normally in this game. Sometimes they "flee" and suddenly, don't want to do that anymore, even if they have an field to flee on left. Maybe the programmer did want to do us an favour, because in some cases you don't get the enemy stone anymore - it is impossible in chess, that would be a so called "Remis".
In reality it is, for example impossible on a normal chess field to get a king with only a king and a knight left, or a king and a bishop left. It isn't possible. The enemy king can always run. Don't believe me - go try it by yourself :)