Phrase for something that is always out or reach/you almost have but never can get

Solution 1:

I can't think of a way to express that without borrowing from literature, so I would probably use 'Holy Grail'. When referring to something other than a girl, it'd probably be 'White Whale'.

Solution 2:

The one-word adjective is elusive, meaning "difficult to find, catch, or achieve," as in "she's my elusive dream-girl".

Solution 3:

There are several possible two-word phrases. But if you kept thinking about dark horse, then maybe wild-goose chase is what you're looking for.

From the Free Merriam-Webster Dictionary,

wild–goose chase noun
a complicated or lengthy and usually fruitless pursuit or search

Solution 4:

This does not quite answer your question (because it is not two words), but the phrase that comes to mind is "so close yet so far away," "so close but so far away," or some other very similar variation of that phrase.

Solution 5:

You might be thinking of the brass ring. The brass ring is originally a reward sought by some carrousel riders, who would try to grab it as they pass by the dispenser. The dispenser also held iron rings, so luck and timing played a big part in the chance of success.

You can find the description in multiple places, including here.

The brass ring is considered elusive, hard to get, a challenge to obtain, and seekers of the brass ring may often end up with the iron ring instead. As a consolation, the iron ring is as worthless as grabbing nothing, by the way.

The brass ring is now a metaphor for a goal that provides ultimate fulfillment in an endeavor and is only achievable by a few.