Ok NEWBIE,
Let me get this straight. If you tune to standard tuning (EADGBe), the guitar will stay in tune no matter what? Correct?
If you tune down half a step or a whole step does it do the same? Stay in or out of tune?
If the guitar really only goes out of tune when in drop C#, I may be inclined to think that the strings get looser and are easier to be influenced by the magnetic pull of the pickups. This is a common problem when you get pickups too close to the strings. Try lowering both pickups some and try again to see if tuning is an issue.