keep on with
keep on with (something)
To continue, persist, or persevere in some action, activity, or endeavor. I know you're discouraged by the reviews, but you really ought to keep on with your writing. You are so talented! I don't know how she kept on with her work in the midst of everything else that was happening in her life.
Farlex Dictionary of Idioms. © 2015 Farlex, Inc, all rights reserved.
keep on with something
to continue with something. Just keep on with your work. Don't pay any attention to me. Can I keep on with this while you are talking?
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs. © 2002 by The McGraw-Hill Companies, Inc.