As long as you continue to learn new things, then no, it doesn't become harder with age. In fact, studies show that people who are lifelong learners can actually increase their ability to learn as they age. Learning, for example, a foreign language in later years has been shown to be just as attainable as in childhood, and might even give some protection against dementia. Your brain can actually become more plastic as you age if you continuously push it to do so.
The idea that learning capacity naturally* diminishes with age seems to be a widely accepted myth (which may have roots in sociological and cultural biases), and the opposite may actually be true.
e: those biases and environmental stressors may also contribute to people becoming less able – or less prone – to try, though, and if you don't use it, you might lose that plasticity. So keep learning.