Okay, I get the issue now. Well, we had to add a host check, because otherwise people were installing the plugin all over the place and activated the auto-updates for dozens of sites without having actually separate licenses.
There is still hope though. If you have any control over the migration process, then all you need is one row from the wp_options table. The option asp_update_data holds the local copy of the key and host, and it is overwritten any time there is a change.
However, when you do a push from the live DB to the dev, if you can, make a copy of that row from the wp_options table, save it somewhere and after the database push just copy it back. That could work without having another license for no reason.