walk heavily and firmly, as when weary, or through mud; "Mules plodded in a circle around a grindstone"
If you say that someone plods on or plods along with a job, you mean that the job is taking a long time. He is plodding on with negotiations Aircraft production continued to plod along at an agonizingly slow pace. to walk along slowly, especially when this is difficult plod through/up/across etc (From the sound or the action)