How repeatable are cognitive science findings within the same individual?
Humans are, as you would expect, much noisier than physical systems. As such, replication of experiments in psychology is very important. Replication provides evidence that the original results were not spurious.

As pointed out in the comments, replication with the same subject pool is not always the way to go. Many tasks have learning effects, and so you would not expect to achieve the same results by re-administering the experiment.

There is a vast statistical literature on reliability testing. A good place to start would be at the Wikipedia article for Reliability (psychometrics)