I gave Letsencrypt a try on one of my servers (x16.webinger.net). So far everything seems to run fine. The certificate was created within the newest Version of Virtualmin, Version 6.01.
Now I ran into a strange Problem that only some iOS Devices (iOS 10, 11). For example iPhone 6s and some iPads do not recognize the letsencrypt certificate as a trustworthy on their standard email app.
I don’t know why you can’t connect via your iOS devices - mine connects just fine.
And like I said, The ONLY thing I can find is that the site supports SSLv3
This does not mean that supporting SSLv3 is the reason for your problem, nor that you have to do anything about it to resolve your problem (although, who knows, it might be related).
Maybe someone else can look and see something we have both missed.
I cannot say, if this is the reason, but you apparently have deployed the certificate for smtp only. If I try to connect to your server to the pop3/imap ports, then I get another (self signed) certificate: