There are many ways to lose a war in Eve, and a lot of the time the way in which you lose a war can indicate the future of your corporation/alliance/coalition. Here are the few most common.
The Abject Surrender
AKA: The "Give Up", The "Fuck This Shit", The "Oh Hell Why Bother"
Epitomized By: IT Alliance
Characteristics: Faced with losing an important battle or the entire war, rather than fight or strategically withdraw, the leaders decide to abandon the war and pull out everything and everyone. Typically to NPC null sec or low sec.
So we've all been there; circumstances have developed such that the enemy has the upper hand and the writing is on the wall, So what does your leadership decide to do? Order everyone to give up, pack up, and move out. This is the ultimate in demoralizing losses, more effective than almost anything the enemy can do.
In some extreme cases, like in IT's defeat, the alliance/coalition disbands on the spot.
Future Outcomes: Most likely is fail cascade, but occasionally you will see alliances rebuild from the loss. Depends a lot on alliance cohesion and the exact circumstances of the loss, i.e. how much blame your side takes for its fortunes.
AKA: The "Oh Shit", The "CVA Special"
Epitomized By: CVA alliance at D-GTMI
Characteristics: In a pitched war or even a losing war, a single big battle can turn around fortunes or end them. In this case, one side goes into a battle and gets beaten so badly, so humiliatingly, that they never properly recover and the war, for all intents and purposes, is suddenly and usually unexpectedly over.
Although CVA didn't officially surrender to AAA after the debacle that was D-GTMI, losing 131 capitals to basically nothing effectively ended the war and no significant fighting occurred there afterwards.
Future Outcomes: Again, Fail Cascade is the most likely outcome as the losers suffer the embarrassment of getting shellacked so badly, but sometimes the pride of trying to fight allows an organization some measure of pride out of the experience.
AKA: The "Never Quit/Never Surrender", The "You Can Pry It From Our Cold Dead Hands"
Epitomized By: Most recently, TEST and Tribes alliances
Characteristics: Faced with steep odds, a side still decides to fight and, although losing, leaves the field with the satisfaction that they fought their best. The biggest difference from The Whelp is that the losers did not fool themselves on the outcome.
Future Outcomes: Losing any war has risk of organizational collapse, but this method of losing has the best chance of alliance/corporation survival. Partly it depends on if the force has space to retreat to for rebuilding and regrouping, and if they are pursued by the winning forces or other hostile entities.