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plug away (at something)
To continue trying or working diligently (at something). I'm really not very good at math, but I've got to keep plugging away if I want to get into an engineering program. John's been plugging away at the new project, but I don't think he's enjoying it very much.
plug away (at something)and peg away (at something)
to keep trying something; to keep working at something. John kept pegging away at the trumpet until he became pretty good at it. I'm not very good at it, but I keep plugging away.