Impersuasible means someone who is not easily convinced or persuaded. Synonyms for this word include stubborn, unyielding, obstinate, unresponsive, unimpressionable, and intractable. Stubborn is a commonly used synonym that describes someone who is determined to cling to their own opinions despite the evidence that contradicts it. Unresponsive is another synonym that suggests a lack of interest or willingness to engage in discussion. Intractable is a synonym often used to describe a problem that is difficult to solve due to its complexity or resistance to change. All of these synonyms illustrate the same trait of being resistant to persuasion, and can be used interchangeably in different contexts.