Sub resources are created inside the root resource using the "new" operator. CDI Dependency injection just cannot work in this case.
The problem: access to Session Beans / CDI managed beans is only possible with a "lookup".
Jersey uses a proprietary extension to to "manage" a custom created class:
[from NetBeans 7 Samples Java Web Services -> REST: CustomerDB Java EE 5]
A ResourceContext should create and integrate the resource as a CDI managed bean. JAX-RS, as well as CDI injection should work in this case.
Essential: the path param @PathParam("customerId") should be directly accessible in the sub-resource via field-injection.