There are mainly a couple of reasons why a messenger (live-chat widget) won't appear when embedded on a website
Most cases the messenger widget won't show because the domain it is on is not whitelisted. You can check from Settings > Inbox > Messenger > Whitelist section:
The embed script is not inserted correctly into the header or footer of the site of which you're installing the messenger on. Please follow the installations steps.
There is a conflict between our messenger script and some other script(s) installed on the same site. We recommend trying to switch scripts/plugins off to pinpoint the effecting script or plugin.