I propose that the causal link here is an evolutionary one and then later reinforced by psychosocial factors leading to future depressive episodes. Because people suffering from GHD were much smaller than their counterparts many many years ago, they were more prone to being attacked by predators. Due to this danger their mental infrastructure had to evolve in a way in which they could become more aware of their surroundings and be alerted to anything out of the ordinary. Detection of possible danger would then lead to the onset of a panic attack and an activation of the vital escape behaviors to save one's hide.
Now that we live in a world where this type of sensory alert system is unnecessary we have many sufferers of GHD also suffering from panic attacks, social phobia, and depression. However, this can be considered an exaptation in the sense that smaller people can be more aware of dangerous bullies rather than hungry predators. A developing sense of helplessness and hopelessness may ensue leading to subsequent depressive episodes.
Nicholas et al. state that short stature alone does not account for the social phobia faced by those diagnosed with GHD. Although a seemingly logical connection, this developing hypothesis indeed needs to be further researched if it is to ever be considered a theory.
Here are some links to previous research correlating panic disorder, depression, and growth hormone deficiency: