In this paper, a real-time ultrasonic attenuation coefficient imaging system identifying cancerous breast lesions is presented. In real-time quantitative medical imaging, spatio-temporal consistency is an important functional requirement, as the inconsistent frame-to-frame quantitative images can degrade diagnostic accuracy. However, the fidelity of an isolated single frame quantitative image is often degraded by the low signal-to-noise ratio due to the short detection time of the RF signal. In order to overcome such problem, the fact that sequential frame-to-frame images have high spatial correlation is utilized. Consequently, a quantitative imaging network featuring an iterative image refinement scheme is designed to inference the difference between adjacent frames images to enhance the spatio-temporal consistency. The proposed system is evaluated through numerical simulation and in-vivo breast cancer measurements. In the in-vivo study, the proposed system demonstrates statistical significance (p-value < 0.05) in the differential diagnosis of breast cancer while achieving 79% less temporal variation.