stay the course - Phrases/Idioms
The American Heritage® Dictionary of Idioms by Christine Ammer. Copyright © 2003, 1997 by The Christine Ammer 1992 Trust. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
Hold or persevere to the end, as in No, he's not resigning; he's going to stay the course. This metaphoric expression, alluding to a horse running an entire race, was first recorded in 1916.