In time-of-flight mass spectrometry (TOF MS), superconducting strip ion detectors (SSIDs) in the parallel configuration are promising for ideal ion detection with a nanosecond-scale time response and a practical large sensitive area. In the parallel configuration, the bias current in one strip is diverted into other parallel strips after each detection event. Under high bias current conditions, the diverted bias current induces cascade switching of all parallel strips. Studies show that cascade switching degrades the ion count rate of SSIDs made from niobium and hence is disliked in TOF MS applications. To suppress the bias current redistribution, we connected resistors in a series with the individual parallel strips using aluminum-bonding wires. Their effect was studied by measuring the pulse height distributions.