every year defective battery

My Yaris will be three years old in July of this year and already has the third new battery inside. Every year when the first really cold nights start, the supposedly brand new battery will give up its mind. What can that be? Besides a marten scare, I have nothing unusual inside. So far, I have always received the new battery as a warranty but if the warranty expires in July, I may be allowed to buy a new one every year. The car dealer finds it not unusual that the batteries are defective after one year, but with my car before (punto) I drove ten years with a battery. It seems to me that this is very strange……….:-( Can I insist that before the end of the warranty the batteries are clarified for which reason the batteries are constantly disconnected? The one?