The phrase 'to stay the course' means to continue to do something or see something through until the end or the completion. Similar in meaning to 'have grit' or to 'stick with it'. This is an informal idiomatic expression used in both social and professional contexts.

1. College was hard, but I was determined to stay the course and get my degree. Looking back now, I'm so glad that I stuck with it.
2. If you're not capable of staying the course when things get difficult then you won't succeed in business. You have to be tenacious in everything you do.

1. If you're not capable of staying the course when things get difficult then you won't succeed in business. You have to be tenacious in everything you do.
2. We have two options here: we can stay the course and hope things improve or, take a risk and diversity.