Dying aristocrat pear tree
This is fairly common with Aristocrat pears and is commonly referred to as incompatible graft union. What happens is a fungal agent, most of the time phytophora, takes up residence in the graft union of the tree and restricts flow of nutrients up an down the trunk. Watering when dry and a pound of 10-10-10 per 100ft2 can help but doesn't always. This does not mean the other one will get it.