Although there are multiple purple nudibranchs, I'm assuming you're referring to Hypseldoris bullocki. You can find more information about them
here. I know of no one that has successfully kept them in captivity (including those doing dedicated research) for a prolonged time. They feed on an unknown type of sponge; some have speculated it may be Dysidea and Aplysilla, but there is nothing to substantiate that thus far. To top it off it's been suggested these have a naturally short lifespan. To clarify though, the Chromodorididae family to which this belongs doesn't have toxins that are released upon death even though that's commonly stated in discussions. The Genus Phyllidia are the ones that have toxic mucus secretions and release terpenes upon death. Unfortunately these are also available in the hobby (bumpy colored nudibranchs). There's plenty of other slugs with known food sources you might want to consider, assuming you want to take the time and necessary precautions for their survival (low current, screened power heads/overflows, constant food source you actively culture ). Take a look at Elysia crispata, Chelidonura varians, or Berghia verrucicornis.
Steve