Hello,
Thank you for your query and we are so sorry about the trouble this must have caused.
Please make sure to install the Rank Math plugin at the Network level and only activate it on the individual site. You may refer to this guide on how to properly install Rank Math on a multi-site environment: https://rankmath.com/kb/installing-rank-math-on-a-multisite-environment/
Then, reconnect your Rank Math plugin to your Rank Math account. To do that, navigate to your WordPress admin area > Rank Math > Dashboard > Help, disconnect and reconnect your Rank Math account.
Please refer to the screenshots below for your reference:
https://i.rankmath.com/ZvEfVb
https://i.rankmath.com/OZSwOw
Once done, please go back to using Rank Math and it should work without any issues.
Hope that helps and please do not hesitate to let us know if you need my assistance with anything else.
Hello,
In this case, please check if thereās some security rule inside your .htaccess file that may prevent saving the settings.
You can also use the default .htaccess file from here: https://wordpress.org/support/article/htaccess/
Please do take a complete backup of your website before modifying your .htaccess as it is a sensitive file.
You may also check if your website has the ModSec (ModSecurity) feature enabled on your server as it can block some bots from accessing your site.
If the issue persists, we might need to take a closer look at the settings. Please edit the first post on this ticket and include your WordPress & FTP logins in the designated Sensitive Data section.
Please do take a complete backup of your website before sharing the information with us.

It is completely secure and only our support staff has access to that section. If you want, you can use the below plugin to generate a temporary login URL to your website and share that with us instead:
https://wordpress.org/plugins/temporary-login-without-password/
You can use the above plugin in conjunction with the WP Security Audit Log to monitor what changes our staff might make on your website (if any):
https://wordpress.org/plugins/wp-security-audit-log/
We really look forward to helping you.
Hello,
Since we did not hear back from you for 15 days, we are assuming that you found the solution. We are closing this support ticket.
If you still need assistance or any other help, please feel free to open a new support ticket, and we will be more than happy to assist.
Thank you.