Sentence:  Long after his cigar burnt bitter, he sat with eyes fixed on the blaze. When the flames at last began to flicker and subside, his lids fluttered, then <WSD>drooped</WSD>; but he had lost all reckoning of time when he opened them again to find Miss Erroll in furs and ball-gown kneeling on the hearthnb.... 
Meaning of the word marked with <WSD> tags:  To slowly become limp; to bend gradually.