Symptom

If you're logged in to wp-admin, the map displays perfectly on your website or page. 
But when you logged out from wp-admin, the map preview is no longer visible on the page and only the search field is displayed. Upon performing a search, it will scroll up to the top of the page and the map will now be displayed. 

Explanation

This could be related to your site caching. 

Resolution

Caching

If you have site caching enabled, you will need to delete your cache or disable your caching plugin to see if the map displays. You may refer to this article that is related to Site Caching. 

CloudFlare

If you have a CDN like CloudFlare, please purge the cache there. If you're using a CDN other than CloudFlare, then please follow the same process on your CDN.

This could also be due to Rocket Loader if you are using CloudFlare. Please follow these instructions to disable rocket loader only for MapifyPro and WooCommerce (and for anything else that uses jQuery):

How To Fix Cloudflare's Rocket Loader Conflict With jQuery | Elegant Themes Help Center (intercom.help)

URL matches to exclude:

https://mysite.com/*mapify*
https://mysite.com/*woocommerce* 

And as always, please purge your Cloudflare cache after doing the above.

SSL

Do have a look at your SSL settings and ensure that they are enabled for your site. The Really Simple SSL plugin for WordPress works great for HTTP to HTTPS redirection to make sure that all of your resources are referenced using HTTPS.

Check Plugins and Themes

Ensure that your Plugins and Themes are up-to-date for your MapifyPro plugin. Following this, you may try to temporarily take out any custom CSS and see if that resolves the issue.