Hi Linda : )
Those plastic cross braces eventually break (weight of lights and
glass, daily thermal expansion, softening from excess heat,
embrittlement from the lighting etc). A strip of stainless steel
riveted underneath the plastic can be used if the break is not at the
very edge. The same metal piece can sometimes be used under the top
trim and over the glass edge to act as a hanger (some of these top
trims are easy to remove and none are structural.
I think what accelerated the crossbrace's demise was the cat trapping
the heat, so the plastic softened, expanded, and couldn't contract
when it cooled because of the glass plates, so after a few cycles of
stretching, it broke apart. Not sure what you can do about your cat,
but making more widely-spaced holes in the light canopy might help.
cheers
NetMax