Hello,
We apologize for the issue you are facing with Google Search Console and Analytics auto disconnecting. This can sometimes happen due to expired authorization tokens or other connectivity issues.
To ensure a stable connection, you can try the following steps:
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Remove Rank Math from Google Account: Go to your Google Account permissions and remove access for Rank Math SEO.

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Reconnect Rank Math: After removing access, go to Rank Math SEO → General Settings → Analytics and click on the Reconnect button at the top.

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Allow Permissions: Make sure to allow all necessary permissions when prompted.

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Configure Analytics Settings: In the Analytics settings of Rank Math, select all values in the drop-down list to configure Analytics properties and then click on Save Changes.

If the issue persists after following these steps, please reply to this ticket with your site URL, and a human agent from our support team will assist you further. Thank you for raising this concern!
Sources:
Resolving Rank Math Analytics Related Issues » Rank Math
Resolving Rank Math Analytics Related Issues » Rank Math
This is an automated reply from Rank Math Support Bot. If you need further assistance, please reply to this topic and a human support agent will reply to you shortly.
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.