So I'm leaving the ducks in, even though they take up about 1/3 of the byte-weight of the game.
Also, the little critter found a bug. In the game itself, you're not supposed to click on the ducks themselves. You just hover the mouse over the ducks, and arrows pop up showing you which way you can move the duck. You then click an arrow to move. Maggie always made it a point, though, of clicking the duck before the arrow. Turns out there's a bug I hadn't noticed.
I do a mouse hit-test on all of the arrows to move the ducks, but all of the arrows aren't always showing. Turns out the hit-test function still returns true if you're over something that's not showing. You wouldn't notice it if you're playing "correctly", but it seems that if you sometimes click where you're not supposed to, you'll click a turned-off arrow and mess up the game.
An extra check to see if the arrow's visible before hit-testing it fixed the problem.
Moral of the story: Don't ship your game until a three year-old tries it. Maybe there is something to the whole "sneezing cat" theory.