A small (but vocal) group of people continuously wonders why we have rejected all attempts to introduce a gender-neutral pronoun. "Why," they ask, "has this not happened, when there is so obviously a need for one?" And really, the question answers itself. Attempts to introduce these new words have failed because language just doesn't work that way.
Words catch on virally. One person uses it, others like it, and it catches on. I suspect most slang words are originated by teenagers and criminals -- people who benefit materially by using words to identify themselves with a subgroup. So the word takes on a certain cachet, because let's face it, most people are basically poseurs.
Really, the only time that "there is a need for this word" actually drives the creation and acceptance of a new word is through jargon. And most jargon originates from one's work or otherwise serious occupation. When you're at work, there's a need to communicate precisely and efficiently. So in other words, people use new jargon terms because they're paid to do it.
Language is a grass-roots effort. Even when things like brand names make it into our vocabulary, it still happens from the ground-up. Nobody at Kimberly-Clark tried to market the word "Kleenex." They just marketed Kleenex. And people were so familiar with the product (and the product itself was so generic) that it was easier to just call all tissue Kleenex.
I guess certain terms will fall in and out of favor for social reasons. In the last 40 years, we've picked up a whole slew of gender-neutral names for professions. But this was more out of necessity than anything else. When you have female firefighters, it's just downright inaccurate to call them firemen.
So what about this gender-neutral pronoun that they keep trying to get us to use? There's no cachet in it; the only people it will help you identify with are irritating pedants. Nobody's paying you to use it. It's not something that you (or your nose) will have frequent contact with. And furthermore, you won't even offend anybody by not using it -- aside from the aforementioned pedants.
So basically, it's useless, does nothing for you, and won't even save you from an awkward situation. And still they wonder why we don't use it? Feh.