無理 isn't so much 'unprofitable' or 'failed' or 'lost' as it is 'pointless' or 'not worth trying'. 無理だった is a statement that an attempt could never have succeeded in the first place, not merely that it failed.
To my ears, there's a clear difference between 負け戦 and 無理な戦. A 負け戦 is simply lost, and that's that; there's nothing else implied about the war. A 無理な戦 should never have been waged in the first place.
Thus,
無理な戦をして、國を縮めてはならぬ。
means something more like 'do not shrink your country (your country's lifespan?) by engaging in a pointless war'. It's not a warning against losing, it's a warning against biting off more than you can chew.