I too have a hen that is an eternal broody, she is 2 1/2 years old. She just hatched 7 chicks last May (wonderful mother BTW) priceless for somebody that wants to hatch chicks but I have already over reached my limit on how many chickens I can and want to have, so so far I have been breaking her broodyness (takes about 4 or 5 days if I catch her early on). She's been broody once since she brooded the 7 chicks so far but I know she will be broody again until the cold weather comes in and she stops laying. She has done that since early on when she was a pullet. As far as I know, there isn't anything we can do to stop them from being broody, picking up the eggs several times a day does not help. This is hormonal and once the hormones set in, they can sit on nothing and brood forever. I love my broody, I actually changed her name to "Ms Broody" now, she is a little pain in the butt because I have to move her into my "nursery" which has AC to keep her cool. Funny thing, she has been there so many times that I think she actually enjoys it because she gets special treats and attention all the time.
Unless somebody comes up with some ideas about how to break a chronic broody, I would say you should probably look into rehoming her with somebody that is interested in hatching chicks, like I said, good broodys are priceless.
Good luck!
