Given that the different parts of our brain are constantly competing for brain real estate and learning requires brain real estate, is it the case that we can only master x amount of skills due to the limit of our brain size? If we train hard enough at something is it possible that that skill can remain with us forever? If so, how much training is required before a skill can become a permanent feature in our brain?
Nothing competes with nothing within our brain. In fact, it's a pretty harmonious machine. Literarily.
It is just a vast network of neurons where a lot of activity happens in parallel. Unfamiliar complex tasks pose greater load on the network (meaning they require activity to spread more and be sustained for longer), and such load may spread into areas that would have done other things otherwise.
Then the brain size is a poor indicator to abilities. Elephants has a brain more than 3 times the size of ours, yet they exhibit a highly limited set of skills compared to humans. It's more about how much stuff there is there, and how is it 'wired'.
Even if you haven't or don't train at all some skills will remain with you forever (or in most people's case, until they die). Like your skill to speak.
But generally speaking, if something becomes a 'skill' it means that it is heavily integrated in our neural network in a way that makes interpretation and execution unconscious processes.
The brain has no native conscious mechanism to forget things (although in some cases and if you know how you can exercise a mild ability to forget).
How long is a piece of string? It depends of what you already capable of doing, how you train, how hard the skill you try to acquire is, etc.
But if I read between the words, then basically you can master any skill you wish, so long it is realistic and you spend the time practicing it. Some people who late in their life became blind later became proficient craftsman - the brain is a wonderful machine, just waiting for you to explore and utilise it.
Given that mastering a skill is often regarded to take 10,000 hours of practice, if you assume 10 hours a day that would be of the order of three years per skill - and assuming a 75 year life span (just to keep the maths easy) would imply the answer's about 25 skills wouldn't it?