It could be reproductive, that is not uncommon. Does her abdomen feel bloated at all, between the legs, below the vent? Is her crop empty, full, hard, soft & squishy, etc?
If your neighbors are poisoning rats, and you get a barn cat, then if the cat were to eat a poisoned rat then the cat could die also, depending on what poison they are using. So that might not be the best solution if they are going to continue with the poison. Are the rats coming from your property? I would work on solving the rat issue, remove and seal up places they are living or hiding, brush piles, debris piles, openings under buildings, try to secure food/feed sources they are attracted too. They can be really hard to get rid of and can travel a fair distance. I had rats coming from a neighbors property (who didn't care) and despite all efforts (since chickens tend to spill food everywhere) we couldn't get rid of them. I had to resort to poison and I poisoned for over 6 months to finally get rid of them. It sucked.
