'plug away' definitions:

Definition of 'plug away'

From: WordNet
verb
Work doggedly or persistently; "She keeps plugging away at her dissertation" [syn: plug away, peg away, slog, keep one's nose to the grindstone, keep one's shoulder to the wheel]
verb
Persist in working hard; "Students must plug away at this problem" [syn: plug, plug away]

Synonyms of 'plug away'

From: Moby Thesaurus