Do animals get Post Traumatic Stress Disorder after escaping from a life threatening situation out in the wild?
Peter Levine speaks to this in his book, "Waking the Tiger:  Healing Trauma".  Most animals in the wild which experience a trauma through natural species interactions will go through a sequence of recovery stages.  

First, when the trauma or death is considered inevitable, the animal will "faint", losing sensory awareness and consciousness. If the trauma or death is averted, the animal will then partially waken out of that faint, and "shake off" the trauma.

This "shaking off" looks remarkably like an epileptic fit, but when the movements are analyzed, they are a muscle-twitch repeat of the sequence of movements that animal took from the time it realized its hazard to the time it fainted. It is this same muscle-twitch capacity which allows human athletes to practice their skills both mentally and physically, without moving from one spot.

Once the "shaking off" is complete, the animal is able to rise and continue its life activities without any longer-term impacts such as PTSD.

Neurologist Dr. Robert Scaer has an explanation for this lack of PTSD.  Lasting trauma is only taken on when the "victim" experiences repeated episodes of the same kind of helplessness and hopelessness.  We humans are very good at giving ourselves and other species repeated episodes of helplessness and hopelessness, and animals which interact with us often pay a price in PTSD.