An HVAC system includes an evaporator. The evaporator includes a sensor configured to measure a property value (i.e., a saturated suction temperature or a saturated suction pressure) associated with saturated refrigerant flowing through the evaporator. The system includes a variable-speed compressor configured to receive the refrigerant and compress the received refrigerant. The system includes a controller communicatively coupled to the sensor and the variable-speed compressor. The controller monitors the property value measured by the sensor and detects a system fault, based on the monitored property value. In response to detecting the system fault, the controller operates the compressor in a freeze-prevention mode, which is configured to maintain the property value above a setpoint value by adjusting a speed of the variable-speed compressor. This prevents or delays freezing of the evaporator during operation of the system during the detected system fault.