Main point: Customers do not need to redeploy or restart in order to force the LCS Client to reconnect.
Marko suggested to replace the 'Connection Grace Period' paragraph with something like:
If your server's LCS connection is interrupted longer than one hour, the server continues to run and enters a grace period that lasts for up to 30 days to allow for reconnection. During this grace period, Liferay DXP displays a warning message to administrators. Upon seeing this message, administrators should follow the troubleshooting steps below.
LCS client app will continually attempt to reconnect to LCS and restore your Liferay instance activation. If it continually fails to connect, check if the server lost access to LCS. See https://customer.liferay.com/documentation/7.0/deploy/-/official_documentation/deployment/lcs-preconfiguration#ensuring-access-to-lcs
If LCS client app stops reconnecting for some reason, you will see no activity in logs. In that case, you can force reconnection by redeploying the LCS client app, following these steps:
1) Remove the Liferay Connected Services Client.lpkg file from the [Liferay Home]/osgi/marketplace folder
2) Place the Liferay Connected Services Client.lpkg file to the [Liferay Home]/deploy folder
If you are still unable to restore connection, please contact Liferay Support.