If you describe something such as an idea or belief as tenacious, you mean that it has a strong influence on people and is difficult to change or remove.
"dogged persistence""dour determination""the most vocal and pertinacious of all the critics""a mind not gifted to discover truth but tenacious to hold it"- T.S.Eliot"men tenacious of opinion"
2. (of memory) having greater than average range;
"a long memory especially for insults""a tenacious memory"