  We study the dynamics of a charge qubit, consisting of a single electron in a
double well potential coupled to a point-contact (PC) electrometer, using the
quantum trajectories formalism. Contrary to previous predictions, we show
formally that, in the sub-Zeno limit, coherent oscillations in the detector
output are suppressed, and the dynamics is dominated by inelastic processes in
the PC. Furthermore, these reduce the detector efficiency and induce relaxation
even when the source-drain bias is zero. This is of practical significance
since it means the detector will act as a source of decoherence. Finally, we
show that the sub-Zeno dynamics is divided into two regimes: low- and high-bias
in which the PC current power spectra show markedly different behaviour.
