Is it permissible to leave fruitful trees unwatered if the father is financially and physically unable to care for them?

If your father's situation is as you described, then there is no blame or disfavor upon him for leaving the aforementioned tree without watering it, because it has no soul, and therefore its upkeep is not obligatory. It is disliked to leave crops and trees without an excuse until they perish, but if the abandonment is due to an excuse, such as the insufficiency of its produce to cover the expense of watering it, then there is no disfavor.