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Related to plug away: defer to, in its entirety, pick up on, come to fruition
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. I plumbed the depths of grief and despair for years after the death of my son; my hope is that I can now help others who are struggling in similar situations.
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.