Hello,
We apologize for the issue you are facing with the modified date not displaying on your posts. It seems that you might need to enable the option to lock or manage the modified date in Rank Math.
Rank Math allows you to prevent the modified date from being updated automatically when making changes to your content. If you want to ensure that the modified date reflects significant changes, you can lock it using the following methods:
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In Gutenberg Editor: Navigate to the Settings panel in your post, find the Lock Modified Date option, enable it, and save your changes.

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In Classic Editor: Go to the Publish section of your post, enable the Lock Modified Date option, and click Update.

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In Elementor: Click the dropdown arrow next to the Publish/Update button and select Update (Lock Modified Date).

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In Divi Builder: Click the dropdown arrow next to the Save button and select Save (Lock Modified Date).

If you have already checked these settings and are still experiencing issues, please reply to this ticket with your website URL so we can assist you further. A human agent from our support team will take over and provide more specific help.
Thank you for raising this concern!
Sources:
How to Lock the Modified Date of Your Posts » 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.