Does the brain get rusty if out of practice? A couple of years back I was in the midst of a lot of competitive exams (for my career, degree etc.). I needed to put my mind to a lot of work. Maths problems, physics problems, logic and GMAT-type questions; you name it.
I haven't been doing these rigorous mental exercises recently. Now, I find that in class I struggle to grasp even the simplest of new concepts.
So, my question: Does the brain lose its edge if out of practice?
(Please state your reasoning. Any references would be appreciated too.)
It doesn't lose its edge; it loses the strength of related associations.

Cognition and skills is very much about memory, and it's all about the neural networks that make up our mental associations.
It might feel like you haven't forgotten anything from the past, but in reality you have forgotten more than you know. 

You are not aware that you have forgotten something until something reminds you of something you can't quite remember exactly. 
Then you might think "I know I used to know this, I know it's somewhere in my head", or you're more like "How did I use to do that?"

Our neural networks (that is, our associations, our memory) will weaken over time if not used. Whenever we think of something, that association will strengthen. The more we think about something, the stronger the association will get, and that is why we can remember by repeating something again and again.

So when you used to study, your associations got strong because you thought about things often. Then you stopped thinking about most of it, and the association(the memory) weakened a lot.

Now you have to train your memory back to where it used to be.