When testing your survey in preview mode you have two options; Researcher Mode and Respondent Mode. To see full explanation of each mode please visit the related article at the bottom of the page.
When in Researcher Mode you have the ability to jump around and forgo any limits or logic you have in place. A reason your skip logic may not be working is because you have it turned off in the mode you are in.
Make sure the "Ignore Skip Logic" box is unchecked.
When in Respondent Mode you will experience the survey exactly how your respondents will and the platform will apply all logic and limits that are in place.
If for any reason you are still experiencing issues with either mode please reach out to firstname.lastname@example.org or click the chat bubble at the bottom right to start a conversation.