No, an electron beam will not lose energy as it travels through a
perfect vacuum. You can imagine a frame of reference in which an
electron is stationary. If the beam were to lose energy in one
reference frame, then an electron would spontaneously accelerate from
rest in a vacuum in this other frame, violating conservation of energy.
Now the space between stars isn't a perfect vacuum. It's full of
photons, dark matter, neutrinos, electrons, protons and a bit of
heavier nuclei. We still don't know much about dark energy, but it's
there too. The photons (a thermal bath with a temperature of about 3K)
will scatter off of the electrons by the Compton scattering process,
slowing electrons down. Eventually, given enough time, the electrons
should come into thermal equilibrium with the photons.
The electrons react much less with neutrinos and dark matter, so we can ignore those to a good approximation.
Vacuum fluctuations do in fact interact with each electron,
contributing to the rest mass of the electron, but in the long haul,
the energy and momentum must be conserved.
(on very short timescales you can observe a different energy of
an electron due to the uncertainty principle, but if you measure the
energy over a long period of time you have to get the conserved
(published on 10/22/2007)