Like many scientific fields, it can take years to build intuition, but it can take only one new idea to tear that intuition down (and hopefully something nice gets rebuilt in its place).
There are some basic exercises you can use to try to build intuition for some paper you're reading and can't seem to penetrate. Here's one that I still do from time to time. Start with a proof that you don't understand but would really like to, which is very long. As you read each paragraph of the proof, try to write a sentence in your own words about what you think the paragraph is saying, in the margins. Hopefully the proof is written well enough that there are well-defined "parts" to the proof ("do X, then define a new function f, then apply X to f, ..."). If not, then from your sentences, separate the proof into your own parts.
Now for each part, try to write a sentence (in your own words) about what each part is doing. At this point, it could be that you find your earlier sentences are not quite accurate or don't fit well together (your intuition was "off"), so you may refine them so they fit logically together. Now you have a few sentences summarizing the whole proof. Then (now this last part is from my advisor, Manuel Blum) try to think of one word or phrase for the whole thing. This phrase would be the key idea that, in your mind, is what gets the whole argument started. (For example, most existence proofs via the probabilistic method can be summed up by: "PICK RANDOM". In the case of $MA \subseteq AM$, I would say something like "MAKE ARTHUR SPEAK MORE". But maybe something else in the proof feels to be the "key" idea to you, which is perfectly fine. It's your intuition!)
I guess my suggestion may be useful for most mathematics, but I found it very useful for TCS, where many proofs really do boil down to 1-2 really new ideas, and the rest is a synthesis of that idea with what was already known.