Remain in one's mind or memory, as in That song has stayed with me all these years. [Late 1500s]
Keep up with; also, concentrate on, continue with. For example, The runner from Kenya stayed with Mark almost to the finish line, or She has an amazing talent for staying with a problem. [Late 1800s] Also see stick with.
Dictionary.com presents 366 FAQs, incorporating some of the frequently asked questions from the past with newer queries.