With my American Standard Strat (stock pickups)* playing through a clean amp, when playing root,5 - root, 6 rhythms on my A and D strings, the fifth and sixth notes do not sound / are undefined / sound mushy / I can't think of any other ways to describe this. This does not occur with any other string pairs, and it does not matter what amp I use. However, these notes do ring out when I play my Strat unplugged, so I do not think it is a resonance problem in the wood. This has been a characteristic of this guitar since I bought it ten years ago, but I am only now getting into this style of music in a serious way.

This dropout happens on all three pickups, and changing the pickup heights does not make a difference. What does make a difference is putting a parametric eq inline, and cutting at 100 hz and boosting at 200 hz with tight Q's on each. In fact, almost everything else I play with this eq setting sounds a lot smoother.

I strongly suspect that this is just the nature of this particular set of pickups. Does that sound reasonable? Is this a common occurrence, and would a new set with a different response curve likely cure this? Or, is this something for which I should consult a guitar tech?

* Also, the pole pieces are not individually adjustable, and this is a left-handed Strat, so the pickups may be backwards. Do stock pickups have a particular orientation?

"...Do stock pickups have a particular orientation?"

Yes, some do.
If the heights appear randomly staggered, then yes, they have to be oriented a certain way.
Is there one pole that is lower than the pickup cover?
Maybe under the "B" string?