Assuming you are in the US, you can sue over anything you want to. But there is a cost to that, and your management company may be banking on that cost being higher than your rent.

Also, if you have all the documents, you should be able to read those and learn what stipulations there are if the lease terminates and you are a month-to-month situation. It could be that you needed to give them more notice. They could have buried it in the fine print. It would suck to pay a lawyer money only to be told “yup, they can do it”, and now you are out more money.