The dissipative dynamics of strongly interacting systems are often characterized by the timescale set by the inverse temperature τP∼ /(kBT). We show that near a class of strongly interacting quantum critical points that arise in the infrared limit of translationally invariant holographic theories, there is a collective excitation (a quasinormal mode of the dual black hole spacetime) whose lifetime τeq is parametrically longer than τP: τeq≫T-1. The lifetime is enhanced due to its dependence on a dangerously irrelevant coupling that breaks the particle-hole symmetry and the invariance under Lorentz boosts of the quantum critical point. The thermal diffusivity (in units of the butterfly velocity) is anomalously large near the quantum critical point and is governed by τeq rather than τP. We conjecture that there exists a long-lived, propagating collective mode with velocity vs, and in this case the relation D=vs2τeq holds exactly in the limit Tτeq≫1. While scale invariance is broken, a generalized scaling theory still holds provided that the dependence of observables on the dangerously irrelevant coupling is incorporated. Our work further underlines the connection between dangerously irrelevant deformations and slow equilibration.