This could also be an air leak under high demand. I.e. a leak not visible at idle, but only under high fuel loads.

At idle the engine isn't demanding a whole lot of fuel. So any air in the system is purged through the return line to your tank. Which would explain why idling seems to temporarily fix the problem. As you get up to speed, eventually your fuel demand will start sucking air through a leaky connection somewhere that eventually increases until you don't have enough fuel to systain the demand of the engine.

My wifes WVO burner was having this problem. I tightened all the clamps on the fuel lines and the problem went away.

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'84 300CD Turbo 132k (Anthracite Grey) - WVO - My daily driver - Recently named coo-coo-coupe by my daughter.
'84 300D Turbo 240k (Anthracite Grey) - Garage Queen
'83 300D Turbo 220k (Orient Red) - WVO - Wifes daily driver

I'm not a certified mechanic, but I did stay at a HolidayInn Express last night.