To directly answer the question: the word is not inherently derogatory (meaning it does not, in and of itself, carry any negative connotations).
Here is the rationale:
Those with with Asperger's use it extensively of themselves (see this answer.) This applies to everyday speech, blogs, communities, public organizations, etc.
It was never meant to be derogatory (it was first used in print by a doctor who has Asperger herself, her blog is aspie.com). So it's different from the reappropriation of the N-word by the African American community and the N-word reasoning doesn't apply.
It is frequently (and neutrally) used in (popular) medical research articles, especially in its adjectival form ("Aspie mind", "aspie brain", etc), instead of the unwieldy "the mind of a person who has Asperger syndrome" or some such. This is simple convenience, not belittlement.
Not surprisingly, no dictionary marks "aspie" as "derogatory" or "rude". Typically it's marked "informal". Urban Dictionary often marks it "affectionate".
That said, if a specific person doesn't want to be called "aspie" (for whatever reason), don't call them that. It's a matter of honoring their wish.
I don't like the diminutive version of my name (and often ask people not to use it), but it does not follow that the diminutive version of my name is somehow derogatory. The simple fact is it's merely diminutive or informal.
Some sources and further reading:
People identifying with Asperger syndrome may refer to themselves in casual conversation as aspies (a term first used in print by Liane Holliday Willey in 1999).
Aspie (also aspie) n. informal a person with Asperger's syndrome
(Oxford American Dictionary)
An aspie is one who has Asperger's Syndrome... Aspie is an affectionate term, and is not meant as a put down.
This term is an affectionate nickname for those with Asperger's syndrome. It was the idea of parents/relatives of aspies.
(Both snippets taken from Urban Dictionary definitions.)
In addition, consider the definition and examples from Oxford Dictionaries:
aspie: A person with Asperger’s syndrome
Cognitive Behavioral therapy is most effective with Aspies because it appeals to their logical nature.
The difference between Asperger's syndrome and the social disorders mentioned above is in the way that Aspies communicate with others.
These examples are obviously not pejorative terms. Judging by their style, they appear to come from some medical research papers, which wouldn't use derogatory terms.
Here is another example from a Kathy J. Marshack, Ph.D., who is a psychiatrist (apparently dealing with the issue on a regular basis):
Families of those with Asperger’s want to know why their Aspies act the way they do.... Aspies have a huge disconnect between thinking and feeling... No matter how much we explain or teach or train the Aspie mind, certain neurological circuits don’t work as they do in the NT brain.
(A) It would be inconceivable for a person of the medical profession to routinely use a pejorative term in a publication about patients.
(B) In the context of the article, she repeatedly uses "aspie" as a neutral, informal term (and also as a convenient adjective), not as a derogatory term in any way, shape, or form. (My guess is, the adjectival form is here to stay, as the alternative is often unwieldy.)
NOTE: The answer is provided based on my research and experience. To err is human, so if you have evidence to the contrary (dictionary definitions, derogatory usage, etc.), please let me know.