Improve visibility to the visitor that a chat response is waiting
If a visitor to the site asks a question and has minimized the chat window while waiting for a reply, It's not readily obvious that a random audible ding notification or the discrete number badge on the chat bubble would grab their attention that they have a reply waiting.
A few potentially simple enhancements to this notification would be:
• If they have minimized the chat bubble ... then just display my reply in a popout like the initial greeting does (See below).
• If they haven't noticed the number badge that there's a reply then maybe gently pulsate, glow, bounce, or grow/shrink the chat bubble to draw the visitors attention to it.