From what I know, currently Weld doesn't have a way to re-inject the @Inject point on activation. Can you please ask this in Weld forum here http://seamframework.org/Community/WeldUsersForum, let's see if they have an idea on how to workaround this issue?
Re-injection is planned, if I'm not mistaken. For a workaround you might get a BeanManager in the @PostActivate and re-inject the fields yourself for now.
Thank you! A JNDI lookup for "java:comp/BeanManager" gives me the BeanManager so that I can retrieve the required "CDI" bean.
I also created a JIRA issue for WELD: https://issues.jboss.org/browse/WELD-848