You're right: the spec says nothing about this limitation - it's only vaguely implied.
From the JAX-WS spec (2.2 Rev A):
The WebServiceContext is treated as an injectable resource that can be set at the time an endpoint is initialized. The WebServiceContext object will then use thread-local information to return the correct information regardless of how many threads are concurrently being used to serve requests addressed to the same endpoint object.
Should be operational over the existence of the endpoint, but only if used in the same thread that setup and stored the request contextual information into thread-local memory storage. Given that WebServiceContext is primarily MessageContext information, which is HTTP Request / Servlet Request / WSDL Operation settings, the thread-local contextual information would probably need to be populated by the thread that initially marshalls the SOAP/HTTP request, meaning that the later async processing thread does not have this info available. Just based on reading - haven't tested this combination.