I've heard that a mare's fertility drops significantly as she ages but she doesn't ever stop cycling.
However, what BB quoted seems likely...but at the same time, wouldn't that imply that the uterus is basically "dead" (unable to function) and wouldn't that possibly be a major source of infection...? Having a "dead" body part stuck inside a healthy one?
AT the same time, the quoted stuff never actually says a mare stops cycling, it just says that she'll generally become infertile. The plot thickens!
OP, did you ever find anything out?