It ends when the cost is so high that automation becomes cost-effective. Basic Income, as much as minimum wage, is a collective push towards skilled labor, away from menial tasks.
In general terms, UBI seems sane. I see two implementation problems. First, worldwide society competition: Can my society support UBI and compete with China? Second, automatic system balancing. What is the correct UBI level? Can we leave it out to be hashed by politicians?