Wiktionary
vb. To keep working at something
WordNet
v. work doggedly or persistently; "She keeps plugging away at her dissertation" [syn: plug away, slog, keep one's nose to the grindstone, keep one's shoulder to the wheel]
Usage examples of "peg away".
Why should a grandson and grandfather peg away at each other with mutual wiolence when all might be bliss and concord.
A notorious beginner of enterprises and non-finisher, partly through lack of time, partly through lack of single-minded concentration, I still wonder how and why I managed to peg away at this thing year after year, often under real difficulties, and bring it to a conclusion.
His body was still shuddering as something snatched the peg away and hurled the door open, spilling him into the dim interior, and something else drove an axe at his head, hard.