First, the official stats, right now, from Area51:
2702 days in beta
5.4 questions per day
Okay – 10 questions per day on average is a healthy beta, 5 questions or fewer per day needs some work. A healthy site generates lots of good content to make sure users keep coming back.
Excellent – 90% answered is a healthy beta, 80% answered needs some work. In the beta it's especially important that when new visitors ask questions they usually get a good answer.
1,371 avid users
24,724 total users
Excellent – Every site needs a solid group of core users to assist in moderating the site. We recommend:
150 users with 200+ rep (currently 1,371 users with 200+ rep)
10 users with 2,000+ rep (currently 148 users with 2,000+ rep)
5 users with 3,000+ rep (currently 99 users with 3,000+ rep)
2.1 answer ratio
Okay – 2.5 answers per question is good, only 1 answer per question needs some work. On a healthy site, questions receive multiple answers and the best answer is voted to the top.
Excellent – 1,500 visits per day is good, 500 visits per day needs some work. A great site benefits people outside the community. Eventually, 90% of a site's traffic should come from search engines.
The above means that we would need more questions per day. The most important of the numbers above, and alas, our weak spot in the statistic. But then, that is among the criteria on the way out – apparently – to consider for graduation.
There seem to be changes for the procedure underway and under the hood and undisclosed as of now. From what I gather: the whole graduation thing will be granularised? Meaning that post-graduation fetures will be addable to a site piece by piece as needed?
But these numbers alone aren't too reliable to predict a site's future, as StartupBusinessSE illustrates.
There are other problems to consider: the danger of being shut down because "graduation doesn't happen" isn't important anymore. Too many 'broken windows' on a site is!.
Positive signs for this site: community moderation is relatively reliable and reasonably quick, in my impression at least. Review queues are emptied quickly, SPAM and trolling often disappears faster than the feed subscription can post it to chat, moderators seem to be doing their job and participate regularly as users as well, with very low indication of mod-fatigue or user complaints (again: my personal impression).
Something not surveyed on Area51 but important indicator for site health would be participation on Meta.History.SE, i.e. here. That is subpar, by quite the margin. Question re-open rate is also on the list of 'improvable'.
As far as I know, the currently still valid official word would be:
Graduation, site closure, and a clearer outlook on the health of SE sites:
When a site starts to consistently receive 10 questions/day, we’ll consider it for graduation.
If a public beta site does not produce consistently helpful content, and lacks the caretakers needed for flags and spam to get handled and our Be Nice policy to be upheld, it will be closed.
To get nearer to the "How to graduate this site", we clearly need more questions per day. And that is more good questions, I might add.
More participation on meta would be nice.
But then, I currently see no real need to really push for it. The WritingSE example indicates a certain level of arbitriness on the one hand and possibly less need overall on the other.
The threat of closure seems far from being a danger for this site.
It seems the other way around compared to what the question assumes: graduation doesn't assure quality, but we have to strive for more content and more quality before we can be considered for graduation.