For war resilience to kick in, you need to be losing against your rival (warscore-wise) but the victor be below of 1.5x of your own NM. So if your NM is 80 and your rival's less than 120 your war resilience will kick in and will stop it from further falling. It is an abstraction of the resilience of a nation (especially useful in defensive wars) into not being subdued, even if they face defeats and lose objective regions. However, if your rival manages to score decisive victories and push that ratio above 1.5x (in our example your own NM less than 80 and/or your rival's above 120) it would stop working and you will continue losing NM until your troops lose almost all their battle-worthiness or riots start erupting in your country as a very low NM will decrease contentment a lot too.
At least, this is how I understood it from the manual, from practice, and from Pocus' formula!
(btw, there is no "war resilience" for the winner, if the winner wants to keep his NM up he needs to score victories continuously)