This is definately hard to prove particular since we are talking about my own perception of my brain. Due to the nature of my career I have never had to stop learning new concepts and skill and the pace of this learning has been pretty constant over the last 25 years.
What I can say is that up until my late 20s this learning did not seem to come at the expense of past learning or memories. Since then I have noticed that while I can still learn new things at around the same pace as in the past, that new learning seems to kick out the old.
Since my ability to learn has not changed (I have had to do courses and other external tests that confirm this personal observation), then the most parsimonious explanation is that new learning is coming at the expense of old learning which is just another way of saying my brain is full :)
Of course it is possible that my memory storage capacity is just getting smaller with age, but if this was the case I would expect it to impact on my ability to learn new things now. My perception is my brain can hold around 30 years worth of learning and as you get old that capacity gets stretched to the point that gaps start to appear. While better than the alternative, getting old is not good :(
