The two-dimensional scaling Ising model in a magnetic field at critical temperature is integrable and possesses eight stable particles A_i (i=1,...,8) with different masses. The heaviest five lie above threshold and owe their stability to integrability. We use form factor perturbation theory to compute the decay widths of the first two particles above threshold when integrability is broken by a small deviation from the critical temperature. The lifetime ratio t_4/t_5 is found to be 0.233; the particle A_5 decays at 47% in the channel A_1A_1 and for the remaining fraction in the channel A_1A_2. The increase of the lifetime with the mass, a feature which can be expected in two dimensions from phase space considerations, is in this model further enhanced by the dynamics.