Just found this site and looks very interesting. I did a little searching around but couldn't find when it was started and when it might go out of beta.
Short answer: we're fairly stable right now, unlikely to graduate soon but more unlikely to be shut down. Sites can take quite some time to make it out of beta, and we are far from the longest time in beta. You can help us get out of beta by spreading the word, sharing good questions and answers to point people here.
We started private beta Jan. 24, 2012 and went public a week later, Jan 31.
You can see some of the site's stats in the right column of the home page:
If you click on the "stack exchange" link, you can compare some of our stats with other SE sites, and if you click on the "Area 51" link on there, you can see a bit more, in particular how we stack up to some of the network's general guidelines:
As you can see, we've been in beta 318 days, we're doing okay on most measures, excellent on our answer rate, and we need more questions.
I've been keeping a regular eye on them for a while now - the questions per day is hovering either side of 2, we've been consistent in maintaining near 100% of the questions answered, and the answer ratio has been on around 2.3 for a while now (so not much at all under the threshold required for excellent in this regard. We also just need a few more casual users with 200 rep to reach the 150 target required for excellent in that repect as well. The visits have been slowly but steadily rising, we were on around 3-400 a day once the initial rush died down.
I think we're around average for a site in beta at this stage - there's definitely a lot of others not doing as well, so while we're not about to graduate that's no big worry. These things take time.