Going back to 2013:
The problem went away after changing both (perfectly serviceable) electric and mechanical pumps. It was never explained, and has not recurred in 1000 hours flying since. My opinion is that the PA 28 fuel system is fundamentally flawed from design onwards and susceptible to minor variations in component behaviour.
My further opinion is that there are many engine failure incidents in PA28’s where a conveniently undetectable cause (carb icing) is attributed when the actual cause is never identified. I’ve never seen the slightest suggestion of carb ice in best part of 2000 Hrs of PA28-161.
I should say say that my loss of pressure never went anywhere the 0.5 psi minimum and certainly didn’t cause any sphincter puckering. But it is something you notice during a long sea crossing!