  Recently an ensemble of nuclear spins in a quantum dot have been proposed as
a long-lived quantum memory. A quantum state of an electron spin in the dot can
be faithfully transfered into nuclear spins through controlled hyperfine
coupling. Here we study the decoherence of this memory due to nuclear spin
dipolar coupling and inhomogeneous hyperfine interaction during the {\it
storage} period. We calculated the maximum fidelity of writing, storing and
reading operations. Our results show that nuclear spin dynamics can severely
limits the performance of the proposed device for quantum information
processing and storage based on nuclear spins.
