The team which decides the fate of SE sites is our "Community Growth" team, which I am not part of. I participate in this site because, like many, I'm a pilot and I love aviation. However, as a developer at Stack, I get to have a lot more conversations with our community team than most of you, so I'll share some of the insights I've gathered to the best of my ability.
Area 51 Metrics
The biggest issue right now is, as you say, question count. Everything else is great. Lnafziger is right that those are not strict requirements for graduation. The reality of it is that those goals are fairly arbitrary. When Area 51 was created, there was an attempt to formalize what criteria would make a good site, but we've learned there's really no way to objectively rate them and every progressive step in a site's life requires human judgment.
Next Step Decisions
The decision on whether to actually permit a proposal, launch a site, graduate a site, or shut it down all tend to be gut decisions supported by the most compelling evidence available. Occasionally we will launch sites against our better judgment... and usually they get shutdown after a few days in private beta. Our community team has gained pretty good intuition over the years about what works and what doesn't.
Why Sites Get Shutdown
The most common reasons for shutting down sites seem to be 1. too much overlap with another site where the same questions would be on-topic, 2. the subject does not lend itself to our Q&A format (too subjective, like Relationships and Dating), or 3. the questions being asked don't interest experts enough that they want to stick around... assuming they were there to begin with.
The first two are pretty easy to spot and those almost never make it out of private beta. The third reason can be harder to spot, and slow growing. answers.onstartups.com succumbed to this problem, and even some of our big sites like Server Fault show signs of this issue. I think that aviation has, so far, done reasonably well with this, but not spectacular. We get questions which community members/experts are interested in, but the question is whether we get enough of that to maintain a base of people who are actively interested in the site.
Sites don't typically get shutdown for low traffic. There might be mixed feelings about this internally, but it generally seems to be our policy in practice. Even if a site is only getting a couple questions per day, if they're good quality, and they get good answers in a timely manner, then it's still making the internet a better place and there's really no reason to shut it down.
A community team member would be so much better equipped to fill out this section, but there are two really big red flags I'm aware of which signal to us that a site is trending downhill: questions going unanswered and moderators abandoning their duties.
If people don't get answers in a timely manner they don't come back. It's also an indication that the experts have either left, or aren't interested in the types of questions being asked. Furthermore, this has a really negative affect on people who arrive here via search (most of our traffic). If they get to a page which is asking the same question they had, but doesn't have an answer, then two things happen. First, they don't develop a positive impression of our site or SE in general. Second, they go back to Google and start clicking other results trying to find an answer. This indicates to Google that the user didn't find what they were looking for and, over time, trains Google to rank us lower in search results - ruining any chance the site had for growth.
Similarly, when moderators stop moderating, the site loses focus and attracts low quality and clutter. The only way for these small sites to be economical is for them to be self-moderating. If SE staff had to moderate them, we would simply shut them down. Remember, we don't even run ads on most of our sites. They generate zero direct revenue. Also, having moderators leave en masse is troubling because they are typically experts who were once enthusiastic about the site, but are apparently no longer interested, which is probably an indirect measurement of quality.
There are many (probably most) of our sites, which will never attract enough traffic to graduate. When the A51 process was created, this wasn't really ever considered. We thought that 1. there wouldn't be nearly as many sites, and 2. the few which made it through would grow big in a matter of months just like Super User and Server Fault did.
In the years since, we've realized that this leaves a lot of sites in a grey area called "beta" where there is a perceived threat of shutdown always looming just over the horizon. We've been contemplating how to address this. One proposal I've heard would amount to a limited graduation where we remove the "beta" label and... nothing else. It would be a recognition that we have no intention to shutdown this site, however it may never be large enough to warrant its own graphic design or the higher reputation requirements for certain permissions which come with traditional graduation. I have no idea when, if ever, we'll implement this, but I wanted to point out that we're aware of how "beta" can stir worries and insecurities in communities.
Small sites which do a good job of self-moderating cost us very little in terms of human or infrastructure, and they give us great good-will in the community. Again, if they're making the internet just little bit better place to find answers, there's no reason to shut them down.
What's the fate of this beta?
To answer your original question as it relates specifically to this site... currently, we're trending slightly upward in visits, but slightly downward in posts. It is, of course, not up to me, but at this rate, I would guess graduation isn't in our future. If we could reverse the downward post trend, I think we would reach graduation eventually. I can't give you an exact questions per day number, or guarantee that's the only thing holding us back, but more than four per day would certainly help a lot. Either way, I don't see any reason to worry that the site is going to disappear. I am consistently impressed by many of our users and the quality of their posts, so I really do believe in this community and that we are making the internet a better place to find answers to aviation questions. That's the point. Whether it says beta at the top of the page isn't the point.