If changes you make to group moderators or senders in the Exchange admin center don't seem to persist, consider the following steps to troubleshoot the issue:
Permissions: Ensure that your account has the necessary permissions to make changes to distribution list settings. Check if there are any role-based access controls or policies affecting your ability to modify these settings.
Browser Cache: Clear your browser cache and try making the changes again. Sometimes, cached data can interfere with displaying the most recent updates.
Different Browser/Device: Try using a different browser or device to see if the issue persists. This helps rule out browser-specific problems.
PowerShell Commands: You can also use PowerShell commands to manage distribution list settings. Connect to Exchange Online PowerShell and use the appropriate cmdlets to update the moderators and senders. This might offer a more stable way to make these changes.
Audit Logging: Check audit logs in the Exchange admin center to see if there are any error messages or events related to the changes you are trying to make. This can provide insights into what might be causing the issue.