"Gonadotropin-releasing hormone (GnRH) stimulates the synthesis and release of gonadotropins, which induce estrogen production and subsequent ovulation. Therefore, long-term GnRH exposure to regulate ovarian hyperstimulation is recognized as the gold standard for most in vitro fertilization (IVF) strategies. However, one of the most disappointing aspects of current IVF technology is relatively low rate (between 35 and 50%) of positive pregnancy outcomes, and the major reason for this high cancellation rate has not yet been revealed. Previous studies have demonstrated that resident stem cell deficiency limits the cyclic regenerative capacity of the endometrium and subsequently increases pregnancy failure rates. Therefore, we hypothesized that long-term GnRH exposure directly damages endometrial stem cells and consequently negatively affects pregnancy outcomes in GnRH-based IVF. In addition to their well-known roles in regulating the hypothalamus-pituitary-gonadal axis, GnRH and its receptors also localize in the extra-hypothalamic endometrium, suggesting a possible non-canonical role in endometrial stem cells. Consistent with our hypothesis, we show for the first time that GnRH suppresses the multiple beneficial functions of endometrial stem cells via the PI3K/Akt signaling pathway in vitro and in vivo."
I found some other sources talking about their use in bodybuilding but they are not nearly as well researched as its use for invitro fertilization. However, if they are seeing that GnRH does suppress cell function through a variety of pathways I think that it would be REASONABLE to assume there may be a similar action in the case you are talking about. As others have said already, being smart about it may be your best bet. Being on large amount of HCG for long periods of time will doubtlessly cause some health issue.