WordPress remembers plugins by folder_name/main_plugin_file_name. So please make sure that both free and premium plugins folder names are not the same. Check it. If the names are different, it should not delete both plugins on deleting one.
If your problem persists even when the folder names are different, then there must be some code which is doing that. In that case, please share your plugins details so we can look into it further!
Thanks!