In reading your problem, my thoughts were from the past, the distant past.
In the old days, with which I am familiar, this would have made me think about the fuel tank vent, or a clogged fuel filter, or fuel pick up screen.
That said, I believe if this were the case in a modern car, a code would be set due to low fuel pressure.
Just food for thought,
'01 C Class, Six Speed
'84 Euro 240D, 523K miles
'88 300E 5 Speed
'81 300D Daughter's Car
Over 800,000 miles in