Welcome to Sustainability SE!
You are right that the question rate of the site is our weakest point.
Moderators have access to all kinds of statistics of the site, but they are not allowed to share those. Instead we've been gathering the public statistics on Area51 and write them down every 2 weeks in this meta post. You can see that the site has been growing slowly but steadily. The number of visits has increased from about 500/month in our first year to 1500+/month right now. Also the number of users with 200+ reputation has grown from 100 at the end of our first year to 200 now. The only thing that stays more or less constant is the question rate, which is usually around 0.6 questions/day. In the stats you can also see that the busiest time of the year is from December to March, with the exception of the Christmas Holidays which is the slowest period (together with July and August).
It's Stack Exchange policy to keep a beta website running as long as there is a group of engaged people that are willing to vote on and answer questions and help improve the site, and I think in that respect Sustainability SE is doing fine. I agree that it will probably take quite some time before this site graduates and looses its beta status.
Personally I think the best way to get our question rate up is to attract more users and we can do that by writing helpful, high-quality questions and answers. Perhaps you can think of sustainability questions you've always wondered about, but never got a good answer and post them. However,
I don't think posting questions just to have more on the site will work because there's a good chance that we'll end-up with low-quality questions. High-quality content is key.
If you have any other suggestions that may help, please do share.
P.S. I know of at least 1 other beta sites that has the same problem. I also keep track of the statistics of Martial Arts SE and that site has more visits/day and more users than we do (it also exists longer), but it
has a slightly lower question rate (around 0.5).