Neutron spectroscopy on the classical triangular-lattice frustrated antiferromagnet h-YMnO₃ reveals diffuse, gapless magnetic excitations present both far below and above the ordering temperature. The correlation length of the excitations increases as the temperature approaches zero, bearing a strong resemblance to critical scattering. We model the dynamics in the ordered and correlated disordered phase as critical spin correlations in a two-dimensional magnetic state. We propose that our findings may provide a general framework to understand features often attributed to classical spin liquids.