Contacting Customers Through Messaging System

Does anyone have problems contacting customers through the Amazon messaging system? It seems like some of my customers never receive messages we send.

Some of our products require delivery appointments and when we can't reach the customer through the Amazon phone number, we have to use the messaging system which is hit or miss. Some customers repsond right away and some seem to never receive the messages. Really wish we were given email addresses and actual phone numbers.