We present a novel implementation of the eventually perfect failure detector ($\Diamond\mathcal{P}$) from the original hierarchy of Chandra-Toueg oracles. Previous implementations of $\Diamond\mathcal{P}$ have assumed models of partial synchrony where point-to-point message delay is bounded and/or communication is reliable. We show how to implement this important oracle under even weaker assumptions using Average Delayed/Dropped (ADD) channels. Briefly, all messages sent on an ADD channel are privileged or non-privileged. All non-privileged messages can be arbitrarily delayed or even dropped. For each run, however, there exists an unknown window size w, and two unknown upper-bounds d and r, where d bounds the average delay of the last w privileged messages, and r bounds the ratio of non-privileged messages to privileged messages per window.