Channel-adaptive random access is proposed to reduce the required transmission power for random access in TDD-based wireless systems. With channel-adaptive random access, a remote station measures the channel state of the downlink, estimates the channel state of the corresponding uplink based on the downlink measurement, and transmits a random access packet only when the channel satisfies a predetermined transmission condition. Thus, transmission is delayed until the channel satisfies the transmission condition. With conventional channel-adaptive random access, a remote station continuously measures the channel state to check if the channel satisfies the transmission condition, which consumes a large amount of power. In this paper, we propose a discontinuous channel measurement scheme for channel-adaptive random access to reduce the power consumption. The performance of the proposed method is investigated in terms of the detection performance of a random access packet, transmission delay, and the power consumption of the receiver.