plod on

To move, progress, or develop at a slow but constant and deliberate pace. John: "Hey Steve, what's new?" Steve: "Nothing much, just been plodding on with my thesis for the last few weeks." My 95-year-old grandfather still makes a point of plodding on to the local shop each morning to catch up with neighbors and friends. I could feel my eyelids getting heavy as the lecture plodded on.