This point has been raised before, but I don't believe it is valid:
1) I've had 5 year old kit wines that showed no evidence of suffering from ill effects from stirring. There was no oxidation, and if the batch had been larger, they'd have aged longer. [wines stop aging when they hit the intestinal tract.]
2) Stirring causes the wine to emit a lot of CO2. Once in the carboy (post stirring) my experience is the wine is still emitting CO2. The wine appears to be insulated from O2 as it is during active fermentation.
My experience is that this is a non-issue. However, if someone can point out a scientific study on the subject, I'd love to read it. Someone actually testing O2 levels would provide a believable answer.
My opinion is just that -- if anyone doesn't want to stir their wine -- don't. Do what you are comfortable with.