Of course I can check a dictionary for the meaning of "maintain" but I don't think the phase "a man who maintains" makes sense as a whole.
The full context:
... a man who knows what he wants, what he stands for, what he will and won't tolerate. A man who's decisive and resolute. A man who maintains.
Gosh, what a horrible website. There's so much good English written, but this isn't it.
Note that in the quote the word "maintains" is written in italics. This indicates that this isn't a standard construction in English, and you'll need to use context. It appears to mean "a man who keeps things steady and doesn't change his mind." He maintains things.
But please. The whole website is just page after page after page of woman-hating bullshit. Avoid.
"Maintain" has various traditional uses, all related to keeping something as it is or holding onto something. As such, it is usually used transitively - for example, "I have a family to maintain", or "he maintains his opinion".
A more modern, intransitive use of the word that matches your example can mean variously to keep one's composure, to be steadfast, or to be unmoveable in whatever the wider context of the statement applies.
