That error is common if the page took longer to display than set by the PHP max_execution_limit or if PHP ran out of the memory allocated to it.
Browsing around your site it seems that the http://www.aapda.org/directory/ page is the the directory home page. This will be the page used in the Customizer preview.
Seeing as you are using the Default template which does not support pagination and it appears you may be displaying 100’s of entries on this page. This could easily cause one or both of the mentioned causes of the error. This is not a bug or limitation with Connections. The same would happen if you were to try to display as many WordPress posts on a single page.
Here’s my suggestion…
In you WP admin edit the http://www.aapda.org/directory/ page.
limit=50 to the existing shortcode so you have something like this:
By limiting the number of displayed entries, hopefully, you will be able to Customizer. If you still get the error, try reducing the limit value.
After you have made the change, remove
limit=50 option from the shortcode.
Seeing your setup, I would highly recommend that you add
force_home=true to the shortcode so the “Back to Directory” link goes back to the map page instead of the http://www.aapda.org/directory/ page which will throw the server error.
Hope this helps, let me know.