We consider a Lévy process reflected in barriers at $0$ and $K>0$. The loss rate is the mean time spent at the upper barrier $K$ at time $1$ when the process is started in stationarity, and is a natural continuous-time analogue of the stationary expected loss rate for a reflected random walk. We derive asymptotics for the loss rate when $K$ tends to infinity, when the mean of the Lévy process is negative and the positive jumps are subexponential. In the course of this derivation, we achieve a formula, which is a generalization of the celebrated Pollaczeck-Khinchine formula.

Keywords: finite buffer, heavy tails, Lévy process, local times, loss rate, Pollaczeck-Khinchine formula, subexponential distributions.