I had the same problem with DAVdroid and Posteo and found the cause, so I wanted to share this:
I am using LineageOS 14.1 on a GT-i9300 (Samsung Galaxy S3) in Austria, my mobile telecommunications operator is A1. As far as I remember I never edited the APN settings after setting up my phone, so I suspect that the default APN for this operator is wrong (sure it’s possible I edited the settings and can’t remember it…). The active APN was named “live!” and used a Proxy – and I ran into the problem described here.
After changing the APN to “A1” (settings with the name of my mobile telecommunications operator and without a Proxy) I can’t reproduce this issue. You can find all APN settings included in LineageOS on GitHub.
BTW, thanks for DAVdroid!!