I am referencing specific named instances in code.

After I do some changes in the code and restart the game, the instances cannot be found anymore.

Error I get: [GMLive][23.12.2023 10:26:38][ERROR] Runtime error: [error] ref instance 103612 (obj_some_obj) does not have a variable `inst_cutscene_move_target`.

I reload the game via game_restart()

I would generally recommend against using game_restart - doing so does not properly clear most of the game state (like global variables, data structures, and so on), and can cause a wide variety of unwanted effects.

For GMLive in particular, this means that a new obj_gmlive is created and has to re-acquire code snippets from the server.