How long can a baby rabbit survive without its mother?

Baby rabbits should not be away from their mother until 8 weeks of age.

In most places this is also laid out as law!

PLEASE do not give away baby rabbits younger than this, the likelihood is they will die.
The first 9 to 11 weeks should ensure your bunny gets nourished enough to leave home. However sometimes rabbits get too attached to their mother and die when they leave her. So 11 weeks is just about your maximum.
The kittens (baby rabbits) can stay with their mother for as long as she'll let them. It's not ideal, though, because it puts strain on the mother. If it's a small litter, and they're looked after properly, they can be weaned as early as about... five weeks. But waiting for six to eight weeks is ideal.

I know that the kittens lose the mother's immunity to disease at around four weeks old. Don't separate them too early of they'll catch diseases.