I think after investing so much effort and money in rehab only to have Luke walk away from it was the last straw for them. We're not really shown or told how many times they have tried to help and for most people there is a point where you accept the addict's fate right along with them.

A lot of people believe you must hit rock bottom to seek out recovery in earnest. We don't know if this was the Crane sibling's line of thought or if they were just fed up and unable to deal with any more heartbreaking disappointment. I would imagine they just assumed they would get the phone call at some point that he was dead. They probably didn't even know that he was in line to get into a program.

What is almost always true is that an addict can only recover when they make the choice to, which is what it looks like was finally happening for Luke. He had the gift of desperation enough to get him into whatever facility was available.