There is some issue as to the actual meaning of night and day. According to some, just because the sun is visible does not mean it is necessarily day.
Regardless, even if day was taken to mean the Sun is visible, this does not mean the Sun would remain visible to everyone at all times over a flat earth.
Why would there not be seasons on flat earth?
Why would there not be solstices on the flat earth?
This is the time where the Sun can be located directly overhead at specific locations on the Earth at high noon.
1. If the Earth is flat, and the Sun is always circling above it, why do we see the Sun set? Even if its "spotlight" isn't shining on us anymore, it should still be overhead, albeit at an angle. But this doesn't happen. We see the Sun approach and pass below the horizon. For this to happen on a flat Earth, the Sun would have to actually pass below the plane of the Earth for us to see it pass below the horizon. But this isn't what the theory says. If the Sun actually were like a giant flashlight, and if we were about to pass outside of its light, shouldn't it appear to grow dimmer and eventually wink out somewhere in the sky?
Furthermore, what causes the Sun to move in a circle in the sky? Newton's first law says that an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. If there were no forces acting on the Sun, it should either sit still or fly off in a straight line. So, there has to be something causing it to move in a circle. The FE Theroy doesn't say what. Is it a massive, invisible object over the Earth's north pole that the Sun orbits around? No, because they don't believe in gravity. Is it some magnetic field that's causing the Sun to move in a circle? No, it couldn't be, because the Sun isn't solid, so there would be nothing keeping the particles in a perfect sphere, and they might stretch out to form some kind of a halo, and our compasses would always point in the direction of the field, which would have to be either towards the ground or towards the sky. Could it be some invisible electric charge above the North pole? No, because the Sun would still stretch out. Could it be the strong or weak nuclear forces? No, they don't act on a macroscopic level. Since there are no natural forces left, could it be a contact force? No, we don't see anything pushing the Sun, and if there were something, it would deform the Sun's spherical shape. Since there cannot be any natural or contact forces making the Sun orbit above the North pole, it is physically impossible for it to be happening. This means that the seasons can't be caused by the expansion and contraction of the Sun's orbit, which doesn't make sense in its own right, because the Sun can't orbit an invisible point above the North pole. So what really causes night and day on a flat earth?
2. The seasons are caused by the tilt of the Earth's rotational axis away or toward the sun as it travels through its year-long path around the sun. The Earth has a tilt of 23.5 degrees relative to the "ecliptic plane" (the line formed by it's almost-cicular path around the sun). An Earth without a tilt would be stratified into climate bands that would get progressively colder as you moved away from the equator. Humans would never survive the continuous winter of the high latitudes, and so the only land we would live on would be the equator. The FE Wiki never mentions a tilt in their seasonal charts and rely on distance from the sun to explain seasons. It is a common misconception that seasons occur because of distance from the Sun, with winter occurring when Earth is farthest away from the Sun, and summer when it is closest to it. However, our planet's distance from the Sun has little effect on the onset of seasons. In fact, Earth is closest to the Sun around the Northern Hemisphere's winter solstice, while it is farthest away from the Sun around the north's summer solstice.
3. The tilt toward the sun is maximized during Northern Hemisphere summer in late June (the "summer solstice"). At this time, the amount of sunlight reaching the Northern Hemisphere is at a maximum. In late December, on the date of the "winter solstice", the Earth's tilt away from the sun is maximized, leading to a minimum of sunlight reaching the Northern Hemisphere. The seasons, of course, are reversed in the Southern Hemisphere. Without this tilt which would be impossible on a flat earth solstices wouldn't exist.