Remain
 

The key word is remain.
If the pitcher was standing there, tossing the ball up and catching it with her non-glove hand (the ball going no more than about a foot up), would you call an IP?

If she's on the pitcher's plate, yes I would. That would probably be the last time she did that, anyway.

So, if the ball accidentally drops from the pitcher's hand while they are on the pitching plate, should that be an IP call? Same rule infraction - ball did not remain in either hand.....

Only if the hands have come together and then have come apart. Pitch don't start til the hands separate.

That has been precisely my ruling on the two occasions I have had this happen in the past (that I remember). The first was a 10U tournament, and the pitcher accidentally dropped the ball while she was standing on the pitching plate, before she had brought her hands together. I called nothing.

The next situation was just about a month ago in a 12U ASA National Qualifier. Had a pitcher who would (quite regularly) toss the ball up in the air and catch it with her bare hand while waiting for the batter to get her sign from her coach. All this was being done within the legal time frame, while she was standing on the pitcher's plate. I called nothing (even though I had a coach yelling from the dugout "Balk! That's a balk!"). I reasoned that because she had not yet brought her hands together, much less separated them, then this was a no call.

However, the rule cited above refers to preliminaries, for which an infraction would result in an IP call according to the book.

Should have shown him the gate. He was either at the wrong game, or too stupid to be allowed to coach young ladies trying to learn the game. :D