Space bearings are widely used in the field of aerospace and they are one of the most fundamental components of space structures. Space bearing failures will cause space machinery breakdown and economic losses, where cage failures are one of the most common faults. Due to low-frequency and small amplitude characteristics of space bearing cage signals, different from faults caused by an inner race, an outer race, and rolling elements, there are a few studies on fault feature extraction of space bearing cages. To address such a remaining challenge, this paper proposes an adaptive chirp mode pursuit (ACMP) for extraction of space bearing cage fault features. Specifically, vibration signals caused by space bearing cage faults can be decomposed into a certain number of signal components, their instantaneous frequencies (IFs), and instantaneous amplitudes (IAs) by using the ACMP. With the help of IFs and IAs, a highly concentrated time-frequency representation can be generated to exhibit fault features of space bearing cages. The performance of our proposed method was validated by experimental vibration signals collected from a flywheel test rig to demonstrate the effectiveness of our proposed method in diagnosing space bearing cage faults and detecting weak fault features.