  We analyze the relaxation of a superconducting flux qubit during measurement.
The qubit state is measured with a nonlinear oscillator driven across the
threshold of bifurcation, acting as a switching dispersive detector. This
readout scheme is of quantum non-demolition type. Two successive readouts are
used to analyze the evolution of the qubit and the detector during the
measurement. We introduce a simple transition rate model to characterize the
qubit relaxation and the detector switching process. Corrected for qubit
relaxation the readout fidelity is at least 95%. Qubit relaxation strongly
depends on the driving strength and the state of the oscillator.
