If an ancient mariner were to say 'Stay the course', what would that statement be in Latin?
"Stay the course" is
… both literally (of ships at sea) as well as metaphorically.
Tenere cursum (suum) = to keep on one's course; commutare cursum = to change course; suo cursu decedere = to deviate from one's course.
(Bonus find from the Packhum Corpus: Tene, Caesar, hunc cursum, et probabitur experimento, sitne feracius et uberius non ad laudem modo sed ad pecuniam principi, si herede illo mori homines uelint, quam si cogantur. – Pliny the Younger, Panegyricus 43, 3: “Hold this course, Caesar [of not stealing people's inheritances], and experience will show whether it is more fruitful and productive not just for the reputation of a Princeps, but also for his wealth, for people to die willingly with him as their heir than if they are forced.” He's not actually talking about the Caesar, by the way, but Emperor Trajan.)