The device-to-device (D2D)-relay mechanism, which works by integrating D2D communications with relay technology, is promising in the future networks. The user pairing is critical to the D2D-relay networks because well-designed user pairing can remarkably promote the system performance. However, most of the existing studies about user pairing mainly focus on the system performance, while the pairing stability, which indicates whether the user pairing is stable and acceptable to users, has not been comprehensively studied. In this letter, we analyze the pairing stability in the D2D-relay networks and propose a metric to quantize it. We also reveal the positive correlation between the proposed metric and the system performance. The numerical results conform to our derivations and show that by keeping the stability metric no less than a threshold, the system performance can reach the expected promotion scale.