A spinster or old maid! What is a similar term for male?

Solution 1:

Confirmed bachelor doesn't necessarily have the same connotation of "not being attractive enough," but it does indicate a sense of permanence. It sometimes is a euphemism for homosexuality, but more generally:

Any man uninterested in committed relationships. (Wiktionary)

A couple more:

• the phrase “confirmed bachelor” describes a man who is having so much fun being single that he’ll probably never marry. (Vocabulary.com)
  
• A confirmed bachelor is a man who shows little or no interest in women. It can be used to suggest that they're gay. (UsingEnglish.com)

As mentioned, homosexuality can be implied, but it is by no means the only way to understand this. For example, a Washington Post headline reads:

Confirmed bachelor and 2016 hopeful Lindsey Graham promises a ‘rotating first lady’

But Graham is not openly gay, and the Post is not insinuating that.

Solution 2:

Lonely old man

Not a single word but this is a common phrase; if you do a Google search the top results are:

• 10 ways to avoid becoming a lonely old man
• The Myth of the Lonely Old Man
• Tips To Avoid Becoming A Lonely Old Man

There is even the notion of lonely old man sitting in a park bench (references).

Solution 3:

I would say that on the shelf conveys both the same meaning and a very similar connotation.

According to the Cambridge dictionary:

If someone, usually a woman, is on the shelf, she is not ​married and is ​considered too ​old for anyone to ​want to ​marry her.

This phrase was initially coined in for women exclusively, but nowadays can be used for men too, although the phrase confirmed bachelor is used (as Nathaniel pointed out).