Loss of power on long drives

I drive a 2001 Mitsubishi Montero 3.5L V6 4WD.

Here is a summary of the symptoms:
• Around town, the car is very responsive and idles well. No problems noticed.
• However, when I drive for a while (25-30 min), the car loses power when gas is applied. The engine will sometimes not respond at all for a few seconds (as though it is flooded or not receiving any fuel) and then will recover, but sputtering without any power.
o There seems to be a connection to the outside temperature. When it rains, or I drive at night, I do not experience these problems, even on very long drives in the mountains.
o It appears to be electrical in some way. I say this because I can “reset” the problem by turning the motor off for only a second and turning it back on. The engine will then run fine for 5-10 minutes before the same symptoms return.
o The car has backfired occasionally when I tried to continue driving the car without “resetting” (see above) the problem.
o It seems to be related to engine load because when the problem occurs I can (at the onset) put the car in neutral and rev it high without problems. Eventually, if I continue to drive, the problem worsens and even in neutral it will sometimes sputter. (I have, though, already replaced the pump just to be sure).
o The air filter was also replaced.