Radar is a critical perception modality in autonomous driving systems due to its all-weather characteristics and ability to measure range and Doppler velocity. However, the sheer volume of high-dimensional raw radar data saturates the communication link to the computing engine (e.g., an NPU), which is often a low-bandwidth interface with data rate provisioned only for a few low-resolution range-Doppler frames. A generalized codec for utilizing high-dimensional radar data is notably absent, while existing image-domain approaches are unsuitable, as they typically operate at fixed compression ratios and fail to adapt to varying or adversarial conditions. In light of this, we propose radar data compression with adaptive feedback. It dynamically adjusts the compression ratio by performing gradient descent from the proxy gradient of detection confidence with respect to the compression rate. We employ a zeroth-order gradient approximation as it enables gradient computation even with non-differentiable core operations--pruning and quantization. This also avoids transmitting the gradient tensors over the band-limited link, which, if estimated, would be as large as the original radar data. In addition, we have found that radar feature maps are heavily concentrated on a few frequency components. Thus, we apply the discrete cosine transform to the radar data cubes and selectively prune out the coefficients effectively. We preserve the dynamic range of each radar patch through scaled quantization. Combining those techniques, our proposed online adaptive compression scheme achieves over 100x feature size reduction at minimal performance drop (~1%p). We validate our results on the RADIal, CARRADA, and Radatron datasets.