Lines 31 through 35 of the poem return to the century's end of the title, using a metaphor to indicate the unpleasant fact that the turn of the century will not, in fact, free the couple from the unpleasantness they have buried. The century is mentioned in terms of one hundred years of accumulation of mud, in which the soles of the couple's boots are stuck forever, making them unable to move forward.
Portrait of a Couple at Century's End