Wiktionary
plug away
vb. (context idiomatic English) To persist or continue, as with an effort.
WordNet
plug away
v. work doggedly or persistently; "She keeps plugging away at her dissertation" [syn: peg away, slog, keep one's nose to the grindstone, keep one's shoulder to the wheel]
persist in working hard; "Students must plug away at this problem" [syn: plug]