Your 11gR1(11.1.1.x) customer does not wish to upgrade to 11gR2 (11.1.2.x) or to 12c (12.1.x) as he probably is not too keen on the new features or is not excited about the cloud yet.
Well, what about support on 11gR1 ? This can be a major factor for upgrade apart from new features!
11.1.1.x Premier support ends June 2015
As per http://www.oracle.com/us/support/library/lifetime-support-middleware-069163.pdf page 36
As per http://www.oracle.com/us/support/library/lifetime-support-middleware-069163.pdf page 36
Note there are three kinds of support - Premier Support, Extended Support and Lifetime Support.
The extended support may not support integrations with new third party vendors and the sustaining support does not include new fixes!
Typically premier support is for 5 years since the launch of the product, extended support for 2 more years and sustaining support thereafter.