What does 'sticking manfully to his guns' mean as it is used in this passage?

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The following is an excerpt from The House of Mirth by Edith Wharton: This novel tells the tragic tale of Lily Bart, a beautiful woman who lives the life of a socialite, even though she herself has no money, and must marry in order to maintain the lifestyle to which she has become accustomed. To do this, she must maintain her reputation as a desirable catch for wealthy suitors.       In the hansom she leaned back with a sigh. Why must a girl pay so dearly for her least escape from routine? Why could one never do a natural thing without having to screen it behind a structure of artifice?... Show more

What does 'sticking manfully to his guns' mean as it is used in this passage?