My MacBook Air is running 10.8 Mountain Lion. I regularly receive security updates (including the pushed NTP fix), as well as application updates like Safari and iTunes, and 3rd party updates for apps like Chrome, Firefox, MS Office for Mac, Evernote, DropBox, Coda, etc.
I don't know what the "official" lifespan of 10.8 is, but it has every appearance of being fully supported by Apple today. And yes, it is very stable.
I loved Mountain Lion and also found it to be very stable. I stayed on it as long as I could, but the new versions of several of the apps I use required Mavericks, and after holding out for a while I upgraded. Mavericks was when I started noticing issues... Graphics driver issues, trackpad gestures randomly not working for periods of time, WindowServer crashing when opening the notification center (wat?), so on and so forth. Mac OS is still my favorite, but I've gotten an irking feeling that in the interest of capturing the mainstream market and making things look pretty and full of features, Apple has skimped on stability and quality. Just my two cents
I don't know what the "official" lifespan of 10.8 is, but it has every appearance of being fully supported by Apple today. And yes, it is very stable.