Yes, when you reconnect the WebSocket, the client will need to call methods to get new instances of any objects it needs. The old stubs are permanently broken.

FWIW the way I've handled this in a React app is, the root stub gets passed in as a prop to the root component, and children call the appropriate methods to get whatever objects they need from it. When the connection is lost, a new one is created, and the new root stub passed into the root component, which causes everything downstream to re-run exactly as you'd want. Seems to work well.