  In p-adic Hodge theory, it is known that if a Galois representation is de
Rham, then it becomes semistable after extension of the base field. Liu and Zhu
asked whether a corresponding result holds in the relative setting: given an
\'etale local system on a quasi-compact rigid analytic variety (for example, a
projective scheme) over a p-adic field, does it become semistable after a
finite extension of the base field? We give a counterexample.
