Original explanation for mechanic was based on balance: "This will prevent folks from sacrificing very much at an early point in the game and then reap the rewards througout [sic] the game."
Initially rate of decrease was 1% per 100 turns, but a lot of players considered that as way to severe and was reduced.
In 1.1.1 and later rate seems to be 1% per 220 turns. Decay happens exactly on turn 220, 440, 660 and so on. On limited testing it seems like piety changing acts do not reset this counter. (Roughly piety value is halved in ~15.000 turns)
While "the piety score can never be lowered below the initial value by this", initial value typically is rather low (~500 gold worth above zero piety). However characters gain some piety on level-ups, so in very early game piety might go up with time despite the decay.