Yes. But the loss of flexibility does not come automatically with age. If you keep moving, you will keep your flexibility. And you can get it back with practice.
I don't think it's as simple as keeping moving. I lost that flexibility fairly early on, certainly in the middle of playing multiple sports through high school, and I'm still very active today.
I know I don't do enough stretching, though. It's just frustrating because my hamstrings never seem to improve, and as soon as I stop stretching, I go back to base (about 12" from touching my toes while standing).
