If you constantly retreat the general, he would be getting the eager to retreat vices I believe.

Retreated general still grants atk/def bonus to the troops. However, due to him being away, they definitely would not get the +2 morale within 50m, though cannot confirm the +1 morale beyond 50m (now it becomes more like 50km).

The AI likes to do that with those general units which are heavily depleted.

*edit*
woot 100 posts

The atk/def bonus dissappears only if the general is killed or captured. Even routed or withdrawn off the field, the atk/def bonus still stays.