Is there a non-technical way to understand why proving confinement is difficult? As far as I understand, the basic reason why we are not able to solve QCD at low energies is because it is a strongly coupled quantum field theory, and a part from exceptional situations in simplified models (involving for instance supersymmetry), we have no tools to fully analyze such regimes. Correct me if I am wrong, but this is a rather technical obstruction.
Is there thus a simple, non-technical reason why proving confinement is such a difficult problem?
 A: The current understanding is indeed that a technical barrier (i.e. the failure of perturbation series due to asymptotic freedom) is complicating the analysis of the low energy regime. 
However, one might look at the problem from a slightly conceptual point of view. The Lagrangian of QCD, which defines the theory, is defined in terms of fundamental fermionic degrees of freedom, which we associate with quarks. At high energies, there is a direct correspondence between those theoretical degrees of freedom and the observable free ones. At low energy, the case is not that simple. The observed degrees of freedom at low energies are hadrons, they are no longer fundamental but show inner structure. The question is now: in which way does the inner structure of hadrons relate directly to the quark degrees of freedom of the high energy theory? There is no clear answer to this question. One may view hadrons as consisting of so-called "constituent quarks", which models baryons as three-quark and mesons as two-quark bound states. As a result of the strong interaction involving gluons, there is no direct correspondence between the quarks in the QCD Lagrangian at high energy and the constituent quarks at low energy.
This might not be the expected answer, but I hope it could nevertheless give some insight into the problem.   
