Despite setting up skip logic, the survey continues to the next question instead of ending as intended. ,
Then your skip logic is wrong. What shall we say without seeing what you have done? Either explain a bit better, or even better, provide us with an LSS file that shows the issue.
But, from what you are telling me, you are actually looking for a "screen out", not a skip logic. You want the survey to end for those, that give a specific answer to a question, correct? In this case we use so called zero quotas to end the survey for them.