Is there any responsibility of the external auditor to evaluate the going concern assumption of the client for more than twelve months of financial statements date?

Yes.   The going concern assumption is the basis of the entire audit process.  If there is any concern at all it is imperative that this is communicated.

When considering audit qestions, remember who you are working for.  It's the shareholders.  Your only task is to make sure that the directors and employees - the people you meet during the audit - are neither criminal nor incompetent.  In other words, what would you want to know if all of the life savings of your entire family were invested in the company you are auditing?