  The role of beamstrahlung in high-energy e+e- storage-ring colliders (SRCs)
is examined. Particle loss due to the emission of single energetic
beamstrahlung photons is shown to impose a fundamental limit on SRC
luminosities at energies 2E_0 >~ 140 GeV for head-on collisions and 2E_0 >~ 40
GeV for crab-waist collisions. With beamstrahlung taken into account, we
explore the viability of SRCs in the E_0=240-500 GeV range, which is of
interest in the precision study of the Higgs boson. At 2E_0=240 GeV, SRCs are
found to be competitive with linear colliders; however, at 2E_0=400-500 GeV,
the attainable SRC luminosity would be a factor 15-25 smaller than desired.
