To arms!
I've noticed this too, and it's been bugging me for some time. I've been giving it a lot of thought and trying to figure out how to solve the issues.
I think there are a number of problems facing the site:
Community Engagement Problems
The demographics are all wrong.
The professional audio community, from what I've been able to gather, is generally quite happy to stay where they are. Most of the online communities for audio that I've found are primarily beginners looking to get started. It's hard to find a lot of real experts, and people who will stay engaged. I think that those who are experts aren't asking a lot of questions, because they don't reasonably expect to find answers.
I'm not sure how to fit SE to the needs of the community
A lot of things that are generally not kosher for Stack Exchange sites are really useful for audio, and I presume video - lists of useful utilities that are aimed at a certain problem, troubleshooting issues that require explaining how something works, and 'soft' subjective answers to somewhat vague questions, like how best to approach a given situation. I think this is because so much of production is as much art as science. Come to think of it though, isn't this largely the same situation faced by sites like Parenting? Can we learn from what they've done?
No evangelists with any reach
I don't know of anyone on the site who has far-reaching influence. We don't have a Jeff or Joel like Stack Overflow, and I don't know how to engage any such people.
Not a lot of experts
I'm currently the highest-rep user on the site but most of what I do is pass on things I've learned from reading. I'm a hobbyist, and most questions I run into can be solved by reading manuals. I'm not providing highly-skilled, professional experience, I'm providing mid-level teaching to beginners.
Scope problems
I was in favor of adding video to the site when that was first proposed, but only because we clearly were't getting traction with just audio production. Honestly, I feel kind of weird when trying to sell the site to the audio communities I associate with, since saying "and video!" seems to dilute the concept. Nobody seems interested. But at the same time, the site wasn't taking off when it was just audio production. I'm honestly not sure what to do here.
I can say that as an audio (but not video) enthusiast, my interaction with the video questions is pretty basic, and I would just as soon have them on a different site. I scan them for moderation issues, but that's the extent of it.
Possible Solutions
Targeting
Honestly, it's not clear to me anymore who, in a few words, the intended audience of the site is anymore. The closest I can come up with is "audio and video production enthusiasts." The image is of a high school A/V club. But if we can figure out who would be interested (say, audio pros and people who want to be them, or video producers, or some kind of hybrid of that), then we can use...
Advertising
I've posted links on forums and in my signature. I help out a lot of beginners on sites like Reddit's music production communities and the Ableton social sites. This hasn't generated us much traffic. We do better with question titles that sound like Google searches.
Honestly, right now, I think the professionals are reading print media. I don't have any data to back this up, but I think they are reading Sound on Sound, not websites. We could try to sell them on the interaction of the site by advertising in these publications. I've not been through a growing SE site before, is there a pattern of doing this that seems to work?
Aim for beginners
The other way to get the site to grow (although this may be shortsighted) is to market it to beginners. Music production is very popular right now due to the rise of electronic music in American culture. The key feature of this is that it can be made on computers, and there are a ton of people out there learning to produce in their bedrooms. In the places I've interacted, lots of people seem interested in "how to do X for beginners." In music, "how do I make a sound like this famous artist" is a very common question online, but we haven't seen a lot of these despite it being all but explicitly allowed here.
I imagine that we'd get traffic and users by going for this crowd, but the downside is that we'll have lots of new, casual users, and it's hard to say if any of them will stick around or respect the site's rules.
Perspective
This is all just how I've seen things, but I realize I'm not necessarily representative of everyone. I'm very much on the audio side of things, and I tend to be focused around a few tools and categories of question. I'm very aware that other people may see it differently, and I'd like to hear from them too.