"Immovable" seems to me to be a word with significant meaning in this text, or at least of significant meaning to Betteredge. Its applied only to three characters - Mr Murthwaite, Sergeant Cuff, and Miss Rachel - but multiple times to each, and has the effect of dramatically setting them apart. Each of those characters is notable in the position of authority they hold over betteredge, and in their inscrutability to him.