Yes, you do get to change stances (second paragraph, page 31). Of note is that the Vigilance stance heals itself at the start of its turn, meaning that all archetypes can spec into the ability to stand themself back up.
A special note for Angel- as mentioned on page 61, the Angel Ability lets them get back up even when damaged, since it heals them.
The primary counter, as I see it, is to avoid focusing damage on foes who will just regenerate off your damage, or by 'wasting' their healing by only dealing small amounts of damage to them - you win by getting everyone to 0 HP, in whichever order that involves.