So, when relics were put in, I'm fairly sure they were intended to be a set of fun, OP items that switched hands frequently and spiced up group combat a little. In practical terms, a few months after implementation, they seem to have become a new means of entrenching the combat advantage of whoever the "top dogs" happen to be, as the vast majority of the time the relics are either sitting with nigh-unkillable denizens or are held by the "top dogs."
Earthshaker, Huskmaker, and the EQ Gem are likely the worst/most noticeable offenders, as they add significant offensive combat advantages, but others (Golden Braid, Luckbinder) are also problematic for the benefits they offer. A situation where those who have the most artefacts / the biggest team can be in a position to get Icons and deny Icons to others, get relics and deny relics to others, etc. is inherently lopsided. Games (like golf, or Super Smash Brothers) introduce "handicaps" for the explicit purpose of evening out playing fields, and in professional sports league drafts, the losing teams after a given season typically receive the top picks in the next draft to compensate. While that has never really been Achaea's MO, the current dynamic could probably use a bit of an adjustment towards this model.
To retain the flavor of the relics (i.e. they make you open-PK and they're a reward for combat prowess) but help spread the fun of using them, I propose a new mechanism - a "possession time" counter that makes it more likely that any given relic will randomly reset from your hands (as they are already designed to do), scaled proportionally with the amount of time that you have held a relic in the past 144 RL hours or so. That way, if people really want to harvest them constantly to maintain a consistent advantage, they'll need to put more work in to do so.
tl;dr: The more you've had a particular relic or any relics recently, the sooner they should randomly repop from your hands.