Websockets Delivery

The question might have been already resolved. Still sharing below:

When chat end-users use a mobile app, they can close or switch between apps. This closes the WebSocket connection. When they return to the app, it reopens the WebSocket connection. However, any messages the agent may have sent to the user, when the user was not in the app, will be missing. To avoid this issue, we recommend using a push notification when the agent sends a new message. This prompts the user to click to open the mobile app. For this you can use the message streaming API to subscribe to the SNS topic and then send a push notification.

https://docs.aws.amazon.com/connect/latest/adminguide/chat-message-streaming.html#how-chat-message-streaming-apis-work