I already switched from Zarafa 7.2.5 to Kopano 8.4 and now everything is running smooth from the outside.
Scientific Linux 7.3
Zarafa 7.2.5 running in dedicated VM with ldap backend (again dedicated ldap VM).
Dedicated VM for Z-push running behind dedicated VM running nginx as reverse proxy, tried z-push versions: 2.2.8/2.3.5/2.3.6/2.4.0.
Zarafa 7.1.4 with z-push from yaffas repo was running under Scientific Linux 6 fine before.
EAS on ipad with iOS 10.2 ran fine.
What did not work, is EAS in Windows Mail in Windows 10 Pro and Windows Mail on Microsoft Lumia 640 phone running Windows 10 mobile. In view that everything is working nice after reinstalling the server with Kopano 8.4, I guess that the fault is in Zarafa 7.2.5 or the way z-push interacts with Zarafa 7.2.5 that is different from Kopano 8.4.
The VM does not exist anymore but I still have the HDD of the VM with logs, if anyone is interested to see the logs. Just tell me, what you are interested in. I guess it should be easy to reproduce the error.