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Wiktionary
stay the course

alt. (context idiomatic English) To persist or continue. vb. (context idiomatic English) To persist or continue.

Wikipedia
Stay the course

"Stay the course" is a phrase used in the context of a war or battle meaning to pursue a goal regardless of any obstacles or criticism. The modern usage of this term was popularized by United States presidents George W. Bush, George H. W. Bush, and Ronald Reagan.