Update Messed It Up

The WordPress plugin updater removes the plugin directory entirely, so you should move your custom icons from the plugin’s directory to a permanent location such as your site’s uploads folder. Then update the custom icons location in AddToAny settings.

They’re currently here (overwritten in plugin updates):
//www.measuringflower.com/wp-content/plugins/add-to-any/icons/custom/

Perhaps move your custom directory into the uploads directory:
//www.measuringflower.com/wp-content/uploads/2015/10/custom/