In wireless cyber-physical systems (CPS), more and more traffic with different priorities is required to be timely transmitted over wireless networks such as 802.11. In order to make full use of 802.11 networks to provide quality of service for wireless CPS, we are concerned with the throughput stability issue (i.e., how much traffic load can be sustained in an 802.11 network). Recent studies on the stability in 802.11 networks have arrived at contradictory conclusions. In this paper, we first delve into the reasons behind these contradictions. Our study manifests that the maximum stable throughput is not simply larger than, less than, or equal to the saturation throughput as argued in previous works. Instead, there exist two intervals, over which the maximum stable throughput follows different rules: over one interval, it may be far larger than the saturated throughput; over the other, it is tightly bounded by the saturated throughput. Most existing related research fails to differentiate the two intervals, implying that the derived results are inaccurate or hold true partially. We then point out that for the parameter settings in the 802.11 enhanced distributed channel access (EDCA) standard, high-priority (HP) traffic can achieve a stable throughput far higher than the saturated throughput, according to the rules we find. This indicates that the prior recommendation by other authors, advocating operating a wireless LAN far below the saturation load to achieve stable throughput and avoid unbounded delay, might be too conservative for many settings. We next propose an idle-sense-based scheme to maximize the stable throughput that HP traffic can achieve, when they coexist with low-priority (LP) traffic. Finally, we ran extensive simulations to verify the effectiveness of the revealed rules and the proposed scheme. This study helps utilize the limited bandwidth of wireless networks fully.