I think you need to use some energy temporarily, although you should be
able to recover it.
It may be that the universe expansion is worse than I thought.
Consider that the computer must, as time goes on, be composed more
and more of empty space, since the density of space is decreasing
(exponentially?). We must signal from one side to the other by sending
something that takes energy, whether gravitational radiation, photons,
or particles. Suppose we send a particle. The problem may be that if we
give the particle too small an initial speed, that it never gets there.
It loses ground due to the universe expanding out from under it, and at
some point it actually starts to go backwards. This means that there
is a certain minimum energy necessary for this kind of signalling, and
that minimum energy will increase as the structure grows larger.
I'm not 100% sure about this but Tipler describes a more moderate effect
like this in a closed universe, and it should be worse in an open one.
Also it's not clear how this generalizes to the other forms of signalling,
but maybe something similar happens.
Hal