keep on phrasal verb ( see also ↑ keep )
1 . to continue doing something, or to do something many times
keep on doing something
You just have to keep on trying.
2 . keep somebody ↔ on to continue to employ someone, especially for longer than you had planned:
If you’re good, they might keep you on after Christmas.
3 . British English informal to talk continuously about something or repeat something many times, in a way that is annoying SYN go on
keep on about
There’s no need to keep on and on about it!
keep on at
If I didn’t keep on at the children, they’d never do their homework.