I would give 2 months minimum there. 30 days is steep.
Whose house is it? Is it an apartment or home? What's your mother's opinion on it?
Dig into why he can't hold employment. Maybe get him into counseling. My mental health system offers help with finding housing, work, etc. Not only does he have trouble holding employment but he has no friends, no coping skills, and is fragile? Sounds like a sad existence, what's going on there. Thankfully he has a support system in a family, but that's about to collapse, and in 30 fucking days no less. Harsh, that's life though!
I understand your plight, I'm dealing with a similar issue in my family. Life is fucking cruel and cold, I get he needs to face reality but be a warm, loving influence as he goes through this. Makes sure he knows the severity of the situation and find resources. He's clearly not thriving as well as you and your sisters, something seems amiss.