Ask HN: Does live chat support really increase conversions?

We run a little e-commerce store and we tried a free live chat software for a month. We saw quite a few chat sessions during the month and we thought we did a decent job. Providing live support is hard because context switching kills productivity but I was hoping live chat would bump our user happiness. Despite our efforts, the conversions for that particular month didn't go up by much.

It was all 9am-6pm live chat with founders themselves, without any scripted answers. We tried to be as prompt as possible. Where exactly did we go wrong? I've seen several blog posts claiming that live chat increases conversions. What has been your experience with live chat on your website? Did it increase conversions? Should we have tried it for longer than a month? Does it work for other industries but doesn't work for b2c online stores?

Thanks