What to do in a chat when a member just stops responding?

When a member stops responding in the middle of a chat, or does not respond for 5 minutes at the start of the chat itself, it could help to check back in to know if the member might want to chat with you later. Let them know you are here for them, and they can connect with you/another-listener any time, whoever is available at their time of need. You can send a message like this to the member:

It seems you could not be here presently, if it might be better to talk at a later time, you can connect with me/another-listener any time, whoever could be available at the time of your need<3

But if they do not respond in another 5 minutes, you are free to move on and leave the chat. You might use the 'end the chat' button too.