Are we playing this right? Influence struggle

By alphagor, in Cold War: CIA vs KGB (original edition)

I just bought the game and played once. Is it normal that we sometimes run out of group cards before cease fire is reached?

If so what happens?

Do we reshuffle the groups and continue playing or do we reach cease fire then?

We seem to often be activating cards until we reach a stalemate and only one player is passing.

In the example given in the rule book why would the second player pass knowing he would loose?

I am missing something for sure...

Struggling with influence :-)

Found my mistake...Thanks anyway. We really enjoy the game.