Should be fixed with 1.8.4.
Account vanishing/missing after device restart
On some Android 4.1 devices or on some Samsung Galaxy S4 – if you install DAVdroid, set up an account and restart your device afterwards the account will be missing.
This behaviour is an Android specific bug and does not rely on the app side. Android is deleting DRM secured apps (paid through Google Play) after a restart on these versions / devices because it checks accounts and apps in wrong order.
Important notice: This is NOT happening on apps that you got via F-Droid.
Fixed by releasing https://play.google.com/store/apps/details?id=at.bitfire.davdroid.jbworkaround (see there)