I suspect that you're using Google. I think that the only way to have it stay off is to make sure that you are logged in. If you don't have an account or don't want one, consider setting up a Google account using an e-mail address created solely for that purpose. As for the steps you need to take, scroll down to find your favourite method on this page:
https://www.wikihow.com/Turn-Off-Google-Safesearch