Where psychology is massively failing to replicate is in trying to characterise healthy individuals. Typically the work of Kahneman.
But that's what interest people and sells, pop psychology.
I'm only tangentially following the whole autism/Asperger's/ADD/ADHD development, and I'm growing more and more convinced that all these categories are mostly arbitrary constructs grown out of random history and academia politics. Happy to be proved wrong here, though.
How do you define science? Could it be a science, according to you, or is there something fundamentally non-scientific about it?
Some fields are quite lucky that the universe is so elegantly organized, but for that isn't true for the overwhelming majority of fields with as many degrees of freedom as biological systems and anything more complex.
That doesn't mean we can't conduct experiments that reproduce.
Science is that which could be disproved.
It is a very small, and very important, part of human knowledge.
See Chalmers' What is This Thing Called Science? for an introduction to these kinds of topics, or Kuhn and Feyerabend's work for historical responses. (And the Duhem-Quine thesis for the "auxiliary hypothesis" response to falsifiability I hinted at with my example.)