Learn English – Name for feeling of death of hope

It's hard to tell exactly what you're looking for. Are you looking for a word to describe:

“a huge discovery into the mystery of existence, the universe and stuff.”

(à la epiphany)? Or are you looking for a word that describes being on the verge of an epiphany, but not quite attaining it?

^{(Perhaps you're in that state right now, and you can't decide which?)}

Anyway, I'll offer two words – one for each. I don't know if these are exact fits, but they seem like they might be close:

satori: (Zen Buddhism) the state of sudden indescribable intuitive enlightenment

Although that word is of Japanese origin, it is found in many English dictionaries. The OED defines it as a sudden indescribable and uncommunicable inner experience of enlightenment, and lists this quotation:

When you have satori you are able to reveal a palatial mansion made of precious stones on a single blade of grass; but when you have no satori, a palatial mansion itself is concealed behind a simple blade of grass.

The second word is of French origin: presque vu. Although not nearly as prevalent in English dictionaries as its counterpart, déjà vu, it describes that I-almost-have-it, tip-of-the-tongue phenomenon. Presque vu literally means “almost seen;” Wikipedia describes it specifically in the context of not being able to recall a word:

presque vu (from the French for “almost seen”) is the failure to retrieve a word from memory, combined with partial recall and the feeling that retrieval is imminent. The phenomenon's name comes from the saying, “It's on the tip of my tongue.”

However, the Urban Dictionary¹ broadens that application somewhat, and defines it almost exactly as the phenomenon you describe in your question:

presque vu: The intense feeling of being at the brink of an epiphany. An extremely frustrating experience, since a breakthrough never arrives - and you are left without it, hoplessly [sic] dreaming it will show itself to you.

¹Not exactly the most authoritative source, I realize

The word you are looking for is SYSYPHEAN. Although rarely used it refers to the legend of Sysyphus, a man punished by the gods by attempting to roll a rock up a hill. No matter how he tried, the rock would roll back down the hill and he would be forced to start over. Used in a sentence it would be; Joe's many attempts at a business were sysyphean since they inevitably failed.