Unwise Child by Randall Garrett

Mike the Angel spent the next three days in a pale blue funk which he struggled valiantly against, at least to prevent it from becoming a deep blue.

There was something wrong aboard the _Brainchild_, and Mike simply couldn't quite figure what it was. He found that he wasn't the only one who had been asked peculiar questions by Snookums. The little robot seemed to have developed a sudden penchant for asking seemingly inane questions.