Luthien: Maia or Elf.

[Hot, crispy nice hobbit]

One can only speculate why Beren preferred life with Luthien to the Gift of Illuvator, afterall they only get to live again for a short while.

Apparently though, Melian remains a Maiar for the rest of her days, even when Thingol was slain.:

Thereafter Melian spoke to none save to Mablung only, bidding him take heed to the Silmaril, and to send word speedily to Beren and Luthien in Ossiriand; and she vanished out of Middle-earth, and passed to the land of the Valar beyond the western sea, to muse upon her sorrows in the gardens of Lorien, whence she came, and this tale speaks of her no more.

However, much more interesting is the fact that even before Melian left Doriath, her power was withdrawn:

But now Thingol lay dead, and his spirit had passed to the halls of Mandos; and with his death a change came also upon Melian. Thus it came to pass that her power was withdrawn in that time from the forests of Neldoreth and Region, and Esgalduin the enchanted river spoke with a different voice, and Doriath lay open to its enemies.

The questionable point here is whether Melian withdrew her power from the realm of her own free will. Perhaps the power of Melian to protect Doriath lay solely on her 'other part' which is her bond with Thingol? Or was it simply that Melian was finally resigned to the fact that Doriath was doomed to destruction? Whatever the reason, there is reason to believe that the 'spirit'/ fea, is the underlying source of power.