We analyze the spontaneous switching between the two N\'eel states of Fe chains on Cu2N/Cu(100), experimentally studied by Loth et al. [Science 335, 196 (2012)]. We show that, in the experimental low-temperature regime (T ~ 1K), decoherence induced by substrate electrons deeply modifies the dynamics of the chain magnetization. The Rabi oscillations associated to quantum tunneling of the isolated chain are replaced by an irreversible decay of considerably longer characteristic time. The computed switching rate is small, rapidly decreasing with chain length, with a 1/T behavior and in good agreement with the experiment. Quantum tunneling is only recovered as the switching mechanism at extremely low temperatures, the corresponding cross-over moving rapidly to further low temperatures as the chain length is increased.