The correction has farther to travel

A prediction moves forward from the first layer to the last. Training begins at the final error and works backward, calculating how much each earlier weight contributed.

A deeper network means more steps on that return journey. At every step, the correction is multiplied by numbers from the next layer.

Think of sound passing through several volume controls. If every control is set below full volume, the sound becomes quieter at each one. In a network, repeated multiplication by small numbers can do the same thing to the correction.

By the time it reaches the earliest layers, there may be almost nothing left to guide them.