A problem exists when an attempt is made to call the fromTheme() method of the QIcon class as a static invocation of a singleton.
E.g.

//header: staticicontest.h
class StaticIconTest : public QMainWindow
{
    Q_OBJECT
public:
    StaticIconTest(QWidget *parent = 0);
    ~StaticIconTest();
private:
    static const QIcon staticIcon;
};
//source: staticicontest.cpp
#include "staticicontest.h"
const QIcon StaticIconTest::staticIcon = QIcon::fromTheme("filenew");

My debugger reports the problem at line 89 of qguiplatformplugin.cpp at a switch statement:
switch(X11->desktopEnvironment)
Perhaps at startup time the X11 object is not yet initialized and is not ready for the call to "fromTheme".
If I made the QIcon non-static, it is able to be initialized as a const in the constructor's initialization list, so I do believe it is the timing of the call, however, I am certainly no expert of the Qt backend.