Social media platforms have emerged as prominent information sharing ecosystems in the context of a variety of recent crises, ranging from mass emergencies, to wars and political conflicts. We study affective responses in social media and how they might indicate desensitization to violence experienced in communities embroiled in an armed conflict. Specifically, we examine three established affect measures: negative affect, activation, and dominance as observed on Twitter in relation to a number of statistics on protracted violence in four major cities afflicted by the Mexican Drug War. During a two year period (Aug 2010-Dec 2012), while violence was on the rise in these regions, our findings show a decline in negative emotional expression as well as a rise in emotional arousal and dominance in Twitter posts: aspects known to be psychological markers of desensitization. We discuss the implications of our work for behavioral health, facilitating rehabilitation efforts in communities enmeshed in an acute and persistent urban warfare, and the impact on civic engagement.