Wireless connection is generally a bad idea for mining rigs. You need fast responses to reduce stale shares. Wireless can give you spiking latencies and could be the cause of why your rig is sometimes displayed as OFF.
I will change "Stability" to "Connection stability", which this actually refers to.
I've never had an issue with it, but I'm adding 8GB more ram to the rig in a few days so I think it will be more stable with regard to your site. Connection wise it's 100% stable. I just have everything else clocked down so low that the added traffic from your site may have pushed the wireless too far on the machine itself.
The only thing that would help is if you connect your rig to internet via cable, not wirelessly.