We consider a coordinated small-cell network in narrow-band deep fading channels, where the transmissions from small base-stations (SBSs) to users usually encounter burst errors. Each SBS has limited cache-capacity via which partial contents can be cached to avoid being fetched from remote cloud and hence reduce the transmission delay. However, due to deep fading, the content transmission may occur numerous burst errors. To solve this problem, in this letter, a meta-based self-supervision learning method is introduced to find the optimal cache policy for minimizing the burst errors. In contrast to the traditional methods, the proposed one has better performance and learning efficiency. More particularly, the proposed can determine much proper cache policy by just training with a few samples of average fading duration of each channel. We demonstrate the effectiveness of the proposed method by numerical simulations which indicate that the proposed meta-learning method is superior to common existing methods in combat of the burst-error problem regarding convergence time and accuracy.