A kinetic model for the ionization processes in high-temperature air in a strong electric field is used to study numerically the mechanism of re-breakdown in a post-arc channel in long non-uniform gaps between a spherical anode and a plane cathode. Our simulation shows two distinct phases of the re-breakdown. The first phase consists of an ionizing wave traversing the gap. After this phase the electrical field in the channel is re-arranged, tending towards being a uniform one. The second phase consists of uniform increases in electron density and gas temperature along the whole channel length. The re-breakdown reduced field increases from 8 to 60 Td when the initial gas temperature T decreases from 3000 to 700 K. The dominant ionization mechanisms in the channel are electron impact ionization of NO at 1000<T<3000 K and of at T<1000 K.