My previous question is regarding why Dumbledore refused to react after learning about Malfoy's celebratory whooping. This question is about why he and Snape together failed to make Malfoy confess his plans. This virtually endangered anybody in the castle for a whole year, given the way Malfoy operated, seriously injuring two students - Katie and Ron.
Snape did try to use Legilimency once and gave up after learning that Malfoy had learnt Occlumency.
Dumbledore to Harry, after he failed to retrieve Slughorn's memory -
"And you feel that you have exerted your very best efforts in this matter, do you? That you have exercised all of your considerable ingenuity? That you have left no depth of cunning unplumbed in your quest to retrieve the memory?"
Harry Potter and the Half Blood Prince, Chapter-20, Lord Voldemort's Request
Why didn't Dumbledore and Snape together "leave no depth of their cunning unplumbed" to get Malfoy to talk and stop the threat he posed to every other person at Hogwarts? Surely they could have outsmarted sixteen year old Draco Malfoy.
As it has been pointed out that Dumbledore was concerned for Draco's life, I am adding the following to clarify what I had in mind.
Had Draco confessed, the Order could have protected Draco, as Dumbledore himself suggested to him, and the rest of Hogwarts would have been saved from his reckless murder plans. So, why didn't Dumbledore use his cunning to achieve that?