peg away at

peg away at

Also, plug away at. Work steadily, persist, as in She pegged away at the tax return until she'd finished, or If we keep plugging away at it, the painting will soon be done. These idioms allude to the persistence required to fasten something by driving pegs or seal something by driving a plug. Peg away dates from the early 1800s plug away from the mid-1900s.
See also: away, peg