The wishlist is an app offered through Shopify and we have no control over issues relating to it. To ensure that your choices are saved, confirm that you are logged into your account on the website so that your wishlist will be saved for later use across all your devices.
If you're having issues try clearing your cookies/cache, use a different browser, or an incognito tab on Google Chrome. If all else fails we also recommend a backup method (like a notepad, text file, or screenshot) to save you searching should your wishlist fail.