Why do Jovian moons fade when transiting Jupiter's shadow?
It's pretty simple, really. The shadow of Jupiter, just like the shadow of the Earth, is not razor-sharp. There is an intermediate region, called penumbra, where illumination is partial. This is due mostly to the fact that the Sun is not a mere dot, but has a measurable size. The fact that the planet itself does not have a sharp edge also contributes a small amount.

http://en.wikipedia.org/wiki/Umbra

Penumbra can be clearly seen during Moon eclipses on Earth. The next one is on April 15 - a few days from today.

http://eclipse.gsfc.nasa.gov/LEplot/LEplot2001/LE2014Apr15T.pdf

http://www.skyandtelescope.com/astronomy-news/observing-news/aprils-total-eclipse-of-the-moon/