The instability for a persistent current switch (PCS) wound bifilarly by a CuNi matrix conductor was studied experimentally and by numerical calculations. The temperature rise due to self-field AC loss during the ramping up of the current causes degradations. The quench current gradually decreases to the adiabatic value, if the current sweep rate is progressively increased. Current transfer from the current terminal to the winding limits the current capacity for the PCS wound by a thick conductor, such as 0.9 mm in diameter. A short ramp pulse causes premature quenches at extremely low currents, which may be due to heat concentration of the self-field AC loss in the conductor outer shell.