Douglas Harper's Etymology Dictionary
1852, from verbal phrase, stick (v.) on notion of "one who sticks in the mud," hence "one who is content to remain in an abject condition." The phrase appears in 1730, in city of London court records, as the alias of an accused named John Baker, who with two other men received a death sentence at the Old Bailey in December 1733 for "breaking open the House of Mr. Thomas Rayner, a Silversmith, and stealing thence Plate to a great Value."
Wiktionary
n. (context mildly insulting idiomatic English) (alternative spelling of stick in the mud English)
WordNet
Usage examples of "stick-in-the-mud".
Most of the time he liked him, felt quite fond of him in fact, but there were other times when he saw him as a narrow bigot, a stick-in-the-mud, who would not give an inch towards progress.
This place needs new stands and a whole new outlook, and what it doesn't need is a fuddy-duddy old colonel for a manager and a stick-in-the-mud Clerk of the Course who can't say boo to a doctor.
His father's an oral surgeon, makes big bucks cutting on people's gums, but he's a stick-in-the-mud.