No matter what you try (including clearing cache and cookies and going into incognito mode), when trying to access your organisation’s ServiceNow, it shows the message ‘You have successfully logged out’ and there doesn’t appear to be any way to log back in.
I have found that a workaround is to select the URL and change ‘external_logout_complete.do‘ and change it to ‘login.do‘. This will present you with a login form. From here, you should reset your password and set up a new one, following the instructions in the email that is sent to you (as you are likely using SSO, which is what this problem relates to). You can then log in as normal each time this happens.
Sometimes simply refreshing the page/logging out of your Microsoft account can fix the issue, but the above solution will guarantee access without having to wait around and hope for the best.