Premium plugins like Borlabs Cookie banner or WPML require a license key for any website they are activated on. So, Suppose you only use a personal single-site license of these plugins, and you use the license key on two different sites: your live and your staging site. In that case, you will run into the issue that the plugin on the live site will recognize the live site as a test site after migrating the staging site to live.
As a result, the plugin will not work anymore as expected, and the license key needs to be reactivated:
The easiest way to prevent this is to purchase a premium license plan supporting at least two websites. Most premium plugins have a business plan that is discounted. So, an extra site will not cost that much.
If you use such a business license with two active sites, the premium plugin will be able to detect both sites properly and will recognize them as different sites. Even after a push, the plugin will stay active on the live site and does not need to be reactivated again.
Get more information about the Borlabs Cookie banner plugin.