No, not always, Bear. Sometimes it is wiser to throw in the towel. I'm thinking back to Germany in the 2WW. We fought until there was no room to fight anymore. We should have given up earlier, and could have saved millions of lives and wouldn't have had a Germany in ashes!
It is not always a sign of heroism and bravery to fight on and on - it is just as often unreasonableness and plain old stupidity and utter disregard for human life.
The same was said about Britain. Britain ended the war worse for wear than Germany. Quite frankly many people thought during the blitz "Its over, we've lost, we can't win, we are just prolonging the bloodshed".
If we get into fact, Germany was still in pretty good shaper come 1945 if not for an increasingly insane hitler trying to dictate tactics over generals and a shortage of Oil.
The motto being, it aint over till its over. Wars are almost always lost do to someone having a lack of resolve, much rarer is a war lost due to the damage inflicted.