Why did Kuro not burn out completely during the bath sequence with Irisviel? In episode 6 of 2wei (not sure where that is in the manga), Irisviel returns to Fuyuki and meets Kuro. She delivers exposition to Miyu, Kuro, and Illya in the Edelfelt mansion's unreasonably large bath. In particular, she informs them that the Holy Grail War is nevermore to be; Kuro does not take this news well, and starts venting mana (or something). 

Anyway, despite Illya's (ahem) mana transfers, Kuro seems to be fading away due to a lack of mana... until she has an emotional moment and admits to herself that she wants to live. 

What is the mechanistic explanation here for why Kuro didn't continue to deplete her mana supplies until she vanished altogether?
Apparently, the fact that Kuro can continue to exist in the world is a miracle created by her own "wish" stated at that same part:

“I want family. I want friends. I want to live a normal, everyday life. But…more than that…more than anything…I don’t want to disappear! I just…I want to live!”

This happens because she is the grail, so she basically granted her own wish as a holy grail, which allowed her to continue living.

Now, this only means Kuro's "wish" stabilized her corporeal form. She still uses the Archer card like the Servants use the class vessels the Holy Grail initially prepares. She doesn't have a mana source and she isn't human, either. She is a miracle that is still allowed to remain in the world.

This is comparable to at least two cases from the original VN: Saber in UBW Good End, and Rider in HF True end. They all still need the mana to stay, same as Kuro.