Does psychology lose it's validity when the subject is versed in psychology? Quite often, I find myself conforming to typical psychological principals, and exhibiting predictable behavior based on external stimuli. However, upon better research of the psychology behind past decisions that I've made, I become more likely to involve psychology theory in future decisions of the same kind. 

But knowing the psychology behind typical decision making processes invariably changes the decision process you experience. It would seem that psychologists should be able to operate in a perfectly logical manner, however, as the saying often goes "All therapists are nuts!"

It's here I feel that traditional psychoanalysis fails. How can you apply psychology and analyze patterns in the thought process of a person if that person is versed enough in psychology to avoid traditional fallacies and pitfalls?

I would be especially interested to see any psychoanalysis studies done purely on psychologists.
There are two different traditions referenced in this question, psychoanalysis and decision making. If by psychoanalysis you mean the tradition of Freud and Jung, my understanding is that it didn't survive first contact with evidence-based practice and is now mainly of historical interest. Maybe some surviving approaches claim their roots in this, I'm not sure, I don't know much about the clinical side of psych.
I do know a little bit about decision making though, the other half of this question, and there knowing the psychology makes surprisingly little difference to people's decisions. You can learn to recognize a base-rate-neglect style question and memorize the answers to the CRT, which will put you in the minority ~20% who tend to get these kinds of questions right, but mostly decision biases are as compelling as perceptual illusions: even knowing that it's an illusion doesn't stop you from seeing the illusion in most cases.
The reason why is probably the same for both! Just like the visual illusions, it looks like many decision-illusions are not so much a flaw in the system as an artifact of how people deal with uncertainty efficiently and effectively using limited resources.

For more on this you might enjoy Kahneman's 'Thinking fast and slow' or Ariely's 'Predictably irrational'. These don't directly address the 'studies on psychologists' thing, but do give lots of examples of hard-to-unsee effects that most definitely persist after reading about them.