What do you call someone who chooses to stay single for life?

Solution 1:

I've heard "confirmed bachelor" for men. The only terms I've heard for women are somewhat derogatory ("old maid" or "spinster"). "Confirmed bachelorette" would be analogous but isn't common yet.

Edit based on comments: apparently "confirmed bachelor" has other connotations in some communities. I don't know how widespread that is; I'd never heard that before.

Solution 2:

Helen Fielding, author of Bridget Jones's Diary borrowed/coined/used the word singleton to fit this bill:

The main focus of plot is Bridget's love life. Her view divides the world into "Singletons," — unmarried and romantically unattached people, of whom she is one — and "Smug Marrieds," by whom she is surrounded.

Here she expounds on the term some in an interview with Ashton Applewhite:

Have men actually learned from it?
Smug Marrieds have, because nobody asks me whether I'm married any more. And no more patronizing comments from my married friends; their attitudes really have changed. It sounds rude to go to a Smug Married and say, "How's your marriage going, still having sex?", but not to go up to a Singleton and say, "How's your love life?" It's great if people realize that there isn't just one way to live. That's an old-fashioned concept, and I think it's losing its grip on us. Life in cities is very similar all over the world, and people do tend to live in urban families as much as in nuclear ones. They're not worse off or better off; the point is that it's no longer abnormal to be single.

One of the pleasures of reading Bridget is the vocabulary you invented. Do you have a favorite word or phrase?
I'm very pleased about the word "singleton," which of course wasn't my word. A friend made it up for a party: "singletons in one hotel, marrieds in another!" "Spinster" is horrible, with connotations of spinning wheels failure. "Singletons" a good word, and it applies to both men and women

Solution 3:

I have, on occasion, heard such men being described using the term bachelor by choice.

Solution 4:

I'm afraid you won't find a currently established word with all the connotations and meanings you require. I think celibate is the closest, because it's the only single-word-term that always has the connotation of choice. The downside to it is its inevitable reference to religion, and I perceive that you aren't looking for that connotation. So it fits with the first three of your criteria.

You'll probably have to make one up. Without the "gay" connotation (if it exists), I think confirmed bachelor/ette is the best proposal so far.

Volitional or discretionary bachelor/ette comes to mind.

For a single word - voluntagamus means literally choice-unmarried in Latin. But I doubt whether you could ever use a personally coined word.