There was a big nature-vs-nurture thread a while back about "talent" that would be worth doing a search for. In this case, though, I like that the question isn't about "talent" in a vague sense but a specific capability, the ability to remember music.
I think the answer is that it isn't necessarily something people are born with, but that it's understandable it wouldn't come easily to you at an older age. This is the kind of thing that falls squarely in the realm of neuroplasticity - the way the brain develops over time as we grow and as it responds to stimulus by growing connections between neurons. Basically, when we do things with our brains, our neurons hardwire themselves into the patterns needed to do those things. The brain does this a LOT, and easily, when we're young (think the old saw about riding a bike); as we grow older, our ability to wire new connections slows down. But connections made young remain, imprinted deep - people with dementia who played piano in their youth will still be able to give a recital of their favorite songs even though they can't recognize their own spouse's face.
So I suspect what you're experiencing is that you're trying to train your neurons to a new task that's unfamiliar - remembering musical patterns - and they're slow to form the links or don't retain them very firmly. That doesn't mean you'll never be able to build that memory - you're not dead yet! - but it will just be a more gradual process. Time and repetition are the key.
I think the answer is that it isn't necessarily something people are born with, but that it's understandable it wouldn't come easily to you at an older age. This is the kind of thing that falls squarely in the realm of neuroplasticity - the way the brain develops over time as we grow and as it responds to stimulus by growing connections between neurons. Basically, when we do things with our brains, our neurons hardwire themselves into the patterns needed to do those things. The brain does this a LOT, and easily, when we're young (think the old saw about riding a bike); as we grow older, our ability to wire new connections slows down. But connections made young remain, imprinted deep - people with dementia who played piano in their youth will still be able to give a recital of their favorite songs even though they can't recognize their own spouse's face.
So I suspect what you're experiencing is that you're trying to train your neurons to a new task that's unfamiliar - remembering musical patterns - and they're slow to form the links or don't retain them very firmly. That doesn't mean you'll never be able to build that memory - you're not dead yet! - but it will just be a more gradual process. Time and repetition are the key.
