When author add new components at Live copy page (For Ex: Inside any component parsys/responsivegrid of column_control..etc)
Author should break the inheritance at Component level for the Live Copy page and needs to add the component. After that when Author do the the roll-out from "Source/Blueprint" page, newly added components content for Live Copy page getting removing.
I remember a customer had raised a similar issue with AEM 6.5.2 where when they add a component on Live Copy and then add the similar component on Blueprint, After rolling out of the Blueprint Page, the similar component got added from Bluprint to Live Copy but the Live Copy component was deleted.
I will add my finding from the case.
1. This was specifically happening with Page Roll Out not Component Roll Out. i.e. with Page Roll Out the Blueprint component was being added to live copy but the live copy one was getting deleted. With Component roll out, the Blueprint component was not getting added to Live Copy.
2. The components that was getting deleted after the rollout procedure was only inside container components.
3. After checking the repository we spotted that local content is still there but the node containing it was renamed with _msm_moved suffix.
4. Because we are shoving the content in container by calling data-sly-resource with a specific name we can't see local content. If that is the situation with you, it means that customization needs to be adjusted to also show the local content even if it is suffixed with "_msm_moved"
You may check this at your end and if needed file a Daycare ticket for better understanding.