* Formal/Political: The peace talks stalled due to the intransigent position of the rebel group, who refused to compromise on their demands.
* Personal/Relationship: Despite her best efforts, Sarah couldn't convince her intransigent brother to help with the family project.
* Descriptive/Historical: The old man's intransigent views on technology made him seem out of touch with modern society.
* Figurative: The rock was like an intransigent obstacle, refusing to budge despite our best efforts to move it.
Remember, "intransigent" implies a stubborn refusal to change one's position or opinion, even in the face of reason or persuasion.