Then, completely out of the blue, the new mother pipes up: "I was wondering if you'd tell me again why Grandpa Flag was called Flag? I know someone told me before when we were little - but I can't remember it properly now."
And whoppee, the answer is EXACTLY what the main character needed to complete the jigsaw puzzle of the plot.
Now, I accept this might happen. But I can't remember asking my mother a question about my family history without there being some sort of lead up to it. And for the previous four pages there hasn't been. This particular question is exceptionally useful, but so lacking in any context it's implausible for it to be there, except for the author's convenience. And at that point the story lost it for me. I couldn't take any of it seriously any more. Which was a pity, because I'd already read over 300 pages.
Convenient writing is the kiss of death for the reader. They've committed themselves to these characters and their story, the last thing they want to be reminded of is that it's all a contrivance. We're trying to create a real world here, with real people doing real stuff. It has to be plausible within its own terms (eg werewolves are fine, so long as what they can and can't do is consistent). One of the wonderful things about Philip Pullman's Northern Lights was that it created a world so real and consistent, it was a surprise that when I came back to my reality I didn't have my own daemon.
It's convenient when the doorbell/phone rings at the crucial moment (unless we've set up a character saying I'll call back tomorrow).
It's convenient when the characters need an X, and a passer by says I happen to have one here.
It's convenient when the missing information is handed to a character without them having to work at it.
In Charlie and the Chocolate Factory, we know that Charlie Bucket is going to find the golden ticket because there won't be much of a story if he doesn't, but he doesn't find it on his first bar of chocolate - that would be convenient. Make the characters - and us - work for their opportunities, and you won't have your readers groaning on the bus.