The disclosed embodiments provide a synchronous switching converter that converts a DC input voltage into a DC output voltage. This synchronous switching converter includes a high-side switching MOSFET coupled between an input node and a first node. The converter also includes a low-side switching MOSFET coupled between the first node and a ground node and is in series with the high-side switching MOSFET. This converter additionally includes a bootstrap capacitor coupled to the high-side switching MOSFET to provide turn-on voltage for the high-side switching MOSFET. Furthermore, the converter includes a main refresh circuit coupled to the bootstrap capacitor and is configured to refresh the bootstrap capacitor during a first operating mode of the synchronous switching converter. Moreover, the converter includes an auxiliary refresh circuit coupled to the main refresh circuit and the bootstrap capacitor and is configured to refresh the bootstrap capacitor during a second operating mode of the converter.