1. to continue to stay in one place. (The on is an adverb, not a preposition.) Everyone else left, but I decided to remain on there. I remained on for a while during the time they were training my replacement.
2. and remain on something to continue to be on something; to continue to serve on a body. Will you remain on the board of directors for another year? I will remain on this committee as long as I am needed.
3. to continue to take a particular medicine. How long should I stay on these pills? I want you to remain on this medication until you run out.
(one's) guard (against someone or something) Go to on (one's) guard (against someone or something).