I have got the same problem, but there must be a problem within SLP, because it works when I am logged in in WordPress and doesn’t work, when I am not logged in.
Here’s my environment, but I have this problem with a total of 5 websites, hosted on different providers.
Store Locator Plus®:5.0.1
Site URL:http://www.lambrettabikes.com
This Info Cached:1523607463
Network Active:No
WordPress Version:5.0.2
PHP Version:7.0.8-0ubuntu0.16.04.3
MySQL Version:5.7.24
PHP Limit:256M
WordPress General Limit:40M
WordPress Admin Limit:256M
PHP Peak RAM:8 MB
PHP Post Max Size:50M