  We prove that the flow map associated to a model equation for surface waves
of moderate amplitude in shallow water is not uniformly continuous in the
Sobolev space $H^s$ with $s>3/2$. The main idea is to consider two suitable
sequences of smooth initial data whose difference converges to zero in $H^s$,
but such that neither of them is convergent. Our main theorem shows that the
exact solutions corresponding to these sequences of data are uniformly bounded
in $H^s$ on a uniform existence interval, but the difference of the two
solution sequences is bounded away from zero in $H^s$ at any positive time in
this interval. The result is obtained by approximating the solutions
corresponding to these initial data by explicit formulae and by estimating the
approximation error in suitable Sobolev norms.
