Apple Tree Life Spans

Do apple trees have a life span? I was home this past weekend and my dad was outside doing yard work and he was giving our apple tree and little "haircut" or just cutting back the branches. We've always had an apple tree as long as I can remember. For the past couple of years though, it has not been producing any apples. Every year the tree will grow the flowers that it produces before actually growing apples, but after the flowers fall off, there are no apples to be found. I just found this to be weird and wondered if there was an actual point when trees just stop producing fruit. This kind of upset me because the apples tasted like no other apple that you can find in your local supermarket. SOOO good! Kind of like how vegetables taste so much better when you grow them in your own garden.