We investigate the concentration dependence of the characteristic relaxation time of dilute polymer solutions in transient uniaxial elongational flow. A series of monodisperse polystyrene solutions of five different molecular weights (1.8×106⩽M⩽8.3×106g∕mol) with concentrations spanning five orders of magnitude were dissolved in two solvents of differing solvent quality (diethylphthalate and oligomeric styrene). Optical measurements with a capillary breakup extensional rheometer of the rate of filament thinning and the time to breakup in each fluid are used to determine the characteristic relaxation time. A criterion for a lower sensitivity limit is introduced, in the form of a minimum concentration cmin necessary for experimental resolution of the effects of polymeric viscoelasticity. This criterion is validated by experiment and comparison to numerical calculations with a multimode bead-spring dumbbell model. These calculations also rationalize previous paradoxical observations of extensional thinning in fluid threads of ultradilute polymer solutions in which stress relaxation apparently occurred faster than predicted by the Zimm theory. Above this minimum sensitivity limit we show that the effective relaxation time of moderately dilute solutions (0.01⩽c∕c*⩽1) in transient extensional flow rises substantially above the fitted value of the relaxation time extracted from small amplitude oscillatory shear flow and above the Zimm relaxation time computed from kinetic theory and intrinsic viscosity measurements. This effective relaxation time exhibits a power-law scaling with the reduced concentration (c∕c*) and the magnitude of the exponent varies with the thermodynamic quality of the solvent. The scaling of this “self-concentration” effect appears to be roughly consistent to that predicted when the dynamics of the partially elongated and overlapping polymer chains are described within the framework of blob theories for semi-dilute solutions.