We are currently in the process of building a completely new infrastructure and have sites and email running completely perfectly except for when a user tries to access the websites via a mobile connection. If the user is connected to their home or office wifi it is fine. If they switch over to their mobile provider then they can not connect. We spent a good couple of weeks in between jobs trying to work out the issue. At first we thought it was the mobile phone networks with out of date cache. Then after 48 hours it pointed to DNS but why would the DNS work on a normal connection and not the mobile. After a lot of Googling and research, our problem was a little more diverse and we followed plenty of red herrings.
It was the SSL certificate on the server. We had installed the wildcard SSL absolutely fine but we did not install the intermediate certificate. As soon as we did that we could visit the sites. Its worth going incognito first and then visiting it on the normal mode. Incognito probably wont used a cached version.