I want to confirm what the lady with the Honda Civic was saying. I have 1998 Civic that I've been driving for about 7 years, from 120K to 255K miles.
I usually let the fuel tank run down low before refilling, at 1/8 of a tank, if the car sits for a more than a few hours, it has to crank over a while to start, like 6-7 seconds. If it has >1/4 tank, either morning or after work it starts no problem, with only 1-2 seconds of cranking.
So it seems to be some kind of pressure bleed out of a one-way check valve or loss of pump prime or drain-back problem of the fuel pump? So it takes time to pump the fuel (or fuel pressure) back up to the engine. BUT only after the fuel drops to some critcal level...
I disagree with Click & Clack, the difference in pressure head between 1/2 tank versus 1/8 tank would be a few inches, that's a tiny pressure head difference. Hard to believe that could affect the starting.