There is a big tree on our property that was already old when we moved in 25 years ago. I've been told it's a Japanese Cherry. It has coppery-red leaves. Many years ago it produced a good crop of small - cherry sized - dark red fruit that was very tasty. Since then it has borne no fruit. It puts up sky-seeking "suckers" from its branches and each year I vainly try to remove them all (getting too old for the climbing- especially if I'm being watched

).
Does it sound as though there's anything I can do to rejuvenate this tree?