working right on through; working nonstop
Describes continuing to work without a break, often with a nuance of perseverance or relentlessness. The で is the continuative form of the copula, linking to a following clause.
He has been working nonstop since morning and hasn't even had lunch.
I worked nonstop yesterday, so I want to rest easy today.
Compound of 働き (continuative form of 働く 'to work') + 通し (from 通す 'to pass through', indicating continuous action) + で (copula continuative).