email domain

We can find a lot of free email account, such as gmail, yahoo etc.
In my institution, we have our own email domain and server.
Many of our member trust yahoo or gmail more than our own. If they have a delay or problem with email, they will directly accuse our own. In fact, I experienced some problem also with yahoo.
So, for what we have our own email domain and server? Our institution don’t need a certain “prestige” of using our own domain. It is just because we have our own website, and we use the facility that is there. Give me idea… shall I close all the email boxes and ask them to have their own free mail?