Keep On Meaning

(idiomatic) To cause or allow to remain in an existing position.

Example:   Keep on trucking!
  Mum, Jimmy keeps on poking me!
1900, Charles W. Chesnutt, The House Behind the Cedars, Chapter I,
  The young woman kept on down Front Street, Warwick maintaining his distance a few rods behind her.
  For goodness sake, will you stop keeping on about it!
  The new boss would like to keep on the present secretary.