  We are interested in the large time behavior of the solutions to the
growth-fragmentation equation. We work in the space of integrable functions
weighted with the principal dual eigenfunction of the growth-fragmentation
operator. This space is the largest one in which we can expect convergence to
the steady size distribution. Although this convergence is known to occur under
fairly general conditions on the coefficients of the equation, we prove that it
does not happen uniformly with respect to the initial data when the
fragmentation rate in bounded. First we get the result for fragmentation
kernels which do not form arbitrarily small fragments by taking advantage of
the Dyson-Phillips series. Then we extend it to general kernels by using the
notion of quasi-compactness and the fact that it is a topological invariant.
