Premium plugins like Borlabs Cookie banner or WPML require a license key for any website they are activated on. So, If you only use a personal single-site license of these plugins and you use the license key on two different sites like your live and your staging site, 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 that supports at least two separate 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 Borlabs Cookie banner plugin.