Yes, airplanes can and do fly all day. According to a report from the Federal Aviation Administration, about five thousand (5000) planes are in the air at any given moment, and more than forty-two thousand (42000) airplanes take flight every day in the United States. However, almost all planes are designed to fly for about twenty-one (21) hours nonstop without any issues. On average, a plane can fly about 3000 hours a year.
Airplanes also have their moments of resting, though, during which their wings, wheels, fuselage, engines, and other structural parts are being serviced. This maintenance process can take weeks or even months. So, planes also rest in between flights. According to a logistic, planes take off or land every 45 seconds on average, which is equivalent to 1300 planes taking off and landing every day at a busy airport. This simply shows that air means of transportation are also always busy all day.