Even near the equinox, when the day length is essentially the same over the entire world, this is possible.
At the equator, not so much; you'd have to average around Mach 1.5, including slowdowns for aerial refueling, to "make the sun stand still", though if you start at dawn and only need to get back by dusk, you gain another 12(ish) hours -- which, however, would still require an average speed of about 1000 km/h. Possible, but having aerial tankers in the right places at the right times, over potentially hostile territory complicates things, not to mention the greatly extended flight path needed to avoid overflying places that don't permit it pushing the required average speed back up to the 1300 km/h range.
But if you fly far enough north or south, you could do this in a Cessna, providing only that you could somehow carry twenty-four hours of fuel. Seems kind of like cheating, like those grade school riddles where you walk an hour south, an hour west, and an hour north and return to your starting point.
But in a fighter jet, with aerial refueling over the South Atlantic and South Pacific, you could circumnavigate at around the 45th parallel without having to overfly anywhere too hostile -- and given 36 hours to fly, only need to average around 600 km/h, which is well below "jet fighter" speed.
