- keep on something
- keep on something1. and keep on Lit. to work to remain mounted on something, such as a horse, bicycle, etc.•
It's really hard for me to keep on a horse.
•It's hard to keep on when it's moving all over the place.
2. Fig. to pay close attention to something. (See also keep on top of someone or something.) •Keep on that story until everything is settled.
•This is a problem. Keep on it until it's settled.
Dictionary of American idioms. 2013.