I have run jchatsocial enterprise with Joomla 3.7. The chat runs on all tested systems and browsers. Only with the Mac with Safari you have to update the chat window manually to see incoming messages. To be sure we have tested it with a 2nd Mac. The result was the same. If other browsers are installed on the Mac, it works. Only we can not provide customers with the browser.

Why is JChatSocial running under Joomla 3.7 PHP 7.1 not on the Mac with Safari and how to fix the error.

I've never heard of such an issue with Mac/Safari, so i've no clue about this and i'm not able to suggest you a possible fix or why this is happening at your end. Safari normally just behaves like any other browser.

BTW if you are able to open the Safari error console and find out some js error, just let me know and maybe i could understand something more. If there are no errors, my only thoughts could be related to some addon or special feature of Safari blocking/suspending the network traffic thus preventing the chat to auto-update.

The version of Joomla or PHP obviously doesn't matter at all.

I do not have a Mac. That's why I gave the assignment to the University of Munich. Tests have shown that Safari disconnects from the Internet as soon as the chat is used and connect with the update button. This happens on all Macs and is reproducible. A screenshot is included.