When ion transport in a binary liquid electrolyte is driven at potentials above the thermal voltage, an extended space charge region forms at the electrolyte/electrode interface and triggers the hydrodynamic instability termed electroconvection. We experimentally show that this instability can be completely arrested in soft colloidal suspension electrolytes composed of low concentrations of polymer-grafted nanoparticles in a liquid host. The mechanism is revealed by means of X-ray scattering, Brownian dynamics calculations, and linear stability analysis to involve overlap of the soft particles at low particle fractions to create a jammed, nanoporous medium that resists convective flow by a Darcy-Brinkman like drag on the electrolyte solvent.