plod away (at something)
To continue to work on, progress through, or develop something at a slow and laborious but consistent pace. A: "How's that new script coming?" B: "I'm still plodding away. I should be finished by tomorrow." I know Janet's been plodding away at her company's tax returns all weekend.
plod away at something
to keep trying to do something. He continues to plod away at writing his novel. It's been three years now. How long have you been plodding away at that book?