Perhaps the stress of deployment and even training disrupts hormone production somehow?

I'd guess that it kicks off growth and regeneration.

Low testosterone in adult men causes pretty severe fatigue and depression that resolves quickly with treatment. You become almost unable to experience joy or desire, so you go through the motions of life with as little effort as possible.

Damage to the brain causes damage to the HPTA. HPTA damage leads to out of "whack" hormones, leading to knock off problems.

Hormone replacement would remedy some of these issues. The same can be seen in people under chronic stress or substance abusers.

> What do you think the mechanism behind this is

Estrogen in the brain is neuro-protective and neuro-trophic. The primary source of estrogen in the brain for men is testosterone converted via aromatase.

However, that's speculative. I found no significant studies on point, notwithstanding physician interest. Because some men seek out testosterone, some doctors might be quick to offer it off-label for other conditions.