Most of your happy customers already told you they'd leave a review, the chat just got closed before anyone asked
Founder here. I run a couple of small products, one of them is Help Desk Hero, a tool that analyzes support chat history (it connects to Crisp right now). Sharing a mistake we made for a long time, mostly because it's obvious once you see it and might be worth a look in your own setup.
Going back through analyzed conversations you keep seeing chats where the customer is genuinely happy, "this fixed my whole problem thank you" happy, and then it just ends. You close it, move to the next one, and nobody circles back to ask for a review. When we counted on one of our other products it was over a thousand resolved conversations that fit, positive sentiment, issue closed, and the number of review requests actually sent from them was basically zero.
The frustrating part is the customer already told you. They said the nice thing, the moment was right there mid conversation, and it closed because asking for a review is easy to mean to do and never get around to when you're heads-down clearing a queue, which as a small team is most days.
Our own product didn't help with this for a while either, which I'll own. We showed sentiment as a percentage on a dashboard and felt good about it, but a number on a chart doesn't change what anyone does, it's just a tidier way to stare at the same pile of chats. So we built a view that flags the resolved conversations that were actually positive and don't already have a review, and lines them up so you can go down the list instead of digging. It also turns the repeat questions buried in those chats into draft FAQs, which was the original reason the tool existed. You still click send yourself, but it turns "remember to do this" into a five minute job.
What I'm curious about is whether this is just us. Has anyone else noticed how many review-worthy conversations quietly slip past, and has it actually cost you? And if you do keep track of which support tickets are worth a review ask, how do you do it, because before we built this we genuinely had nothing.