Chats disappear automatically from the agent's sidebar. Because of this, agents are unable to create new incidents directly from the chat window.
This should happen at 10:30 AM PST.
There is an OOB Scheduled Job "RemoveConversationsforClosedRecords" which closes the conversation if the related record (chat_queue_entry, incident, hr case, etc.) is inactive.
Since this was added to mitigate performance issues that can happen if agents don't close out their chats, we do not recommend turning this off completely.
Instead, if your agents need more time to work on the chats, you can edit the job to run less frequently like once a week on a weekend.