Why do patients taking gnrh-a lose bone?

GnRH hormones. While normally gnrh stimulates sex hormones, it achieves this only when it is secreted in bursts by the hypothalamus. When given in injections, it circulates continuously and it suppresses the hormones that in turn stimulate the ovary in women and the testes in men. As a consequence, there is a lack of sex hormones (estradiol in women, testosterone in men, leading to bone loss as in menopause.
Shuts down brain. Gnrh ends up shutting down your brains production of hormones. The pituitary then does not make lh and fsh and your ovary does not make estrogen. And the lack of estrogen affects your bone.