Does a generic connection depend continuously on its curvature?

For a principal bundle with semi-simple structure group over a smooth four-dimensional base manifold, the set of connections (gauge potentials)A which are uniquely determined by their curvature (field or field strength)F is generic in the set of all potentials, endowed with the Whitney C^∞ topology. However, the operator taking each such field F to its potential A is not continuous. Partial negative results are given concerning the existence of a smaller generic set on which this operator is continuous.