We recently experienced this issue when a mistake in the server room cut power to a number of machines. But, our Web Adaptor machine has been rebooted many times in its life cycle, and this is the first time we've seen the WebAdaptor.config file empty itself. After re-registering was unsuccessful, we reinstalled the Web Adaptor, and the issue was resolved.
I contacted Esri support for more information, and learned that this is a known Web Adaptor bug:
BIG-000083324 The ArcGIS Web Adaptor unregisters or loses its configuration, and resets to the default or blank configuration.
I was told it is resolved in version 10.3. The issue was described to me as inconsistent--they don't know exactly what circumstances produce this bug, only that it is related to cut power. In our situation, it was an unplanned event and all prior planned reboots were fine. Also worth noting: in our case, this affected a machine on which both ArcGIS Server and the Web Adaptor are installed.
I hope that helps!
And here are the rest of the details Esri gave me:
Web Adaptor unexpectedly unregisters or loses its configuration and resets
to the default or blank configuration. A brief glitch in network
connectivity between the GIS Server and the Web Adaptor can cause the Web
Adaptor to unregister itself from the GIS Server. This results in a Web
Adaptor that has no configuration and thus can no longer communicate with
the GIS Server. This issue has been addressed in the 10.3 release. The
check between the GIS Server and Web Adaptor now has additional tests to
overcome these minor glitches in network connectivity and avoid an
erroneous unregister of the Web Adaptor.