1
general::
1. Persevere or persist at doing something. For example, If you keep at your math, you'll soon master it. It is Also put as keep at it, as in He kept at it all day and finally finished the report. [Early 1800s] 2. keep at someone. Nag, harass, or annoy someone, as in You have to keep at Carl if you want him to do the work, or He keeps at Millie all the time. Also see KEEP AFTER.
American Heritage Idioms
2
general::
Phrase(s): keep at something
to persist at doing something; to continue trying to do something. • John kept at his painting until the whole house was done. • Keep at the job if you want to get it finished., Phrase(s): keep at someone (about something)
Go to keep after someone (about something)., Phrase(s): keep someone at something
to make sure someone continues to work at something. • Please keep Walter at his chores. • I was so sick I couldn’t keep myself at my work.
McGrawhill's American Idioms And Phrasal Verbs