continuing effort to achieve something despite difficulties (persistent)
Heated and irritated as he was by his spasmodic toil at the pumps, for all his first nameless feeling of forbearance the sweating Steelkilt could but ill brook this bearing in the mate; but somehow still smothering the conflagration within him, without speaking he remained doggedly rooted to his seat, till at last the incensed Radney shook the hammer within a few inches of his face, furiously commanding him to do his bidding.
There are no more uses of "dogged" identified with this meaning, but check unspecified meaning below.
Show samples from other sources
She worked with dogged determination.
High achieving students often succeed because of their dogged effort.
’The White Whale—the White Whale!’ was the cry from captain, mates, and harpooneers, who, undeterred by fearful rumours, were all anxious to capture so famous and precious a fish; while the dogged crew eyed askance, and with curses, the appalling beauty of the vast milky mass, that lit up by a horizontal spangling sun, shifted and glistened like a living opal in the blue morning sea.