What exactly does CalDAV-Sync do?
According to the fix app, the actual bug it fixes is 34880.

Basically, Play installs paid apps to the wrong location, specifically to /mnt/asec instead of /data/app.  When the service cache is generated on boot, that location is not yet mounted, so the service and the associated accounts gets removed.

This works around that by using the same account on a non-paid app, which installs normally, get picked up by the service cache, and this prevents the account from getting removed.