[shadowgovt]

It's the physics of the arrangement of satellite, sun, and Earth. The satellites are only visible due to reflected sunlight, and they're flying quite low for satellites, i.e. near to Earth. The nearer an orbital object is to Earth, the larger percentage of the arc of its orbit is occluded by the Earth's shadow.

Given their close proximity to Earth, they can reflect sunlight at dawn and dusk (when the sun is shining "along" the surface relative to the observer) but when an observer is in nighttime (i.e. within Earth's shadow), Earth blocks the path of light to reflect off the satellites and they won't shine. Hypothetically, they could still pass in front of distant objects and occlude them, but I'm assuming based on the way the problem is described that flooding a telescope with reflected light is more of a problem than occluding a distant object for a few moments.