Isn't this a continuation of a campaign started by an eligible President Bush?
IIRC, the authorizations for deployment are limited to 90 days unless specifically authorized by Congress. I don't know whether the authorization for continued deployment in Afghanistan had any time limitations or whether it was open ended. If it was open ended then it was effectively a declaration of war and Larkin is screwed. If it required a request for extention at any time since Obama became president then Larkin would have a valid reason to demand proof of eligibity before deployment. It all depends on whether this is still Bush's war or whether it is now Obama's war.