What Android is capable of abandoning the mission. He is the owner of that Android... regardless he is baby or adult baby, he is still the master...
That actually raises an interesting question about how androids operate in this world.
They don't seem to have the same rights (or at least aren't treated) as humans, otherwise she wouldn't have been on sale at a secondhand store, but can they go against their owner (in the sense of refusing orders) if it conflicts with their programming? Are owners allowed to force androids to do as they please?
There's also the matter of Koutarou never having given her specific instructions/orders. As soon as she was turned on he already pretended to be a baby and was expecting her functions as a babysitter android would simply automatically do the rest. So she's not really going against anything right now since Koutarou never talked to her about being her owner or anything.
All in all they're kind of in a limbo at the moment. Koutarou keeps Makina in the dark so Makina only has her babysitter programing to rely on, so she does what she knows best, however she keeps finding conflicts with her knowledge of babies (obviously), so she's kind of lost on how to proceed, and Koutarou isn't guiding her.
I wonder if they'll ever explore the relationship between androids and humans in this world.