Approximating the Tail
If the long term dependency is significant, it will be because of extra events which come from sustained bursts.
Simulation with a short-term generator at higher load may be a reasonable approximation to behaviour during bursts.
So, use a series of simulation runs to construct e.g. a short-range load against loss curve;
Use a Hurst-based model for a load/probability distribution, and integrate to estimate loss rate.