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.