I think I'm lucky that I was never a highly skilled golfer, and that I did not start trying to play regularly (other than just once every five years or so and an "outing") until I was in my early 50s. I'm 70 now. Today I had my best round (lowest medal score) in nine or ten months, but still managed to come up a little short on the match money side. I putted exceptionally well today. Maybe I'm getting better at that (but realisticly, probably not), so there's hope. I don't care what my handicap is. It is what it is. I don't measure my enjoyment of the game that way.
I frequently play with older men, in their 80s, who use to be scratch or close, and are continually frustrated by the fact that they can't score like the used to, and now hit more "bad" shots than the used to. Skillwise I'm level with some of them now, and thrilled about where I am, while they're not. One guy, now 92, shot his age at least three times last year, yet is often gloomy about his game. As far as I'm concerned, if you in your 90s and shooting your age, you are a damn good player, no matter what you think.
As you get older your skills will surely decrease, and for many reasons it will happen at different ages for different people. However, if you define "getting better" as I like to, as learning more about yourself, how to manage the game you have, how to enhance your skills at your reduced physical/mental capabilities and how to enjoy the game, then I think you can always get better.