To resolve the issue of not being able to save recipes and the recipe box disappearing on your Apple desktop, follow these steps:

1. Clear Browser Cache and Cookies: A common solution for login loops is to clear your browser's cache and cookies. Here’s how to do it in Safari:
- Open Safari.
- Go to the Safari menu and select Preferences.
- Click on the Privacy tab.
- Click on Manage Website Data.
- Select Remove All to clear cookies and cache. Then click Done.

2. Update Your Browser: Ensure you are using the latest version of Safari or any other browser you prefer. Outdated browsers can cause compatibility issues. To check for updates:
- Click on the Apple icon in the top left corner.
- Select System Preferences.
- Click on Software Update.

3. Login Properly: If you are facing persistent login issues:
- Visit the New York Times Cooking website directly.
- Ensure you are entering the correct email and password associated with your New York Times account.
- If you're using Apple Sign In, ensure your Apple account is correctly linked. You can do this by visiting the relevant settings in your Apple account and unlinking it, then trying to log in again directly with an email and password combination learn more.

4. Use a Different Browser: If the issue continues, consider using an alternative browser like Chrome or Firefox to see if the problem persists there.

5. Check Internet Connectivity: Ensure that your internet connection is stable and functioning properly, as connectivity issues can cause problems with logins.

6. Disable Chrome Extensions (if applicable): If you are using Chrome and have any extensions (like ad blockers), try disabling them temporarily to see if that resolves the problem learn more.

7. Reach Out for Support: If none of the above steps work, consider reaching out to NYT support for further assistance. The troubleshooting guide from the New York Times can provide additional help learn more.

After following these steps, check if you can access your recipe box and save recipes successfully. If the situation still doesn't improve, additional technical support may be necessary.