There is an excellent answer by Gilles, on Meta.SE that talks about the growth pattern of a community.
A dip in activity after the private beta is common. Quoting from that answer:
The sites that fail in private beta start are mostly the ones that peter out on day 2. The sites that fail in public beta are the ones where there is no growth at all and the existing community drifts off. The flat bit at the beginning of the public beta can last for many months; as long as an engaged community remains active, there isn't really a time limit.
This nicely fits in with the new graduation announcements and how SE looks at site outlooks:
Thanks to many devoted users, it’s grown clear that smaller SE sites can do a great job of maintaining themselves and producing high quality Q&A. Not every site is going to be a blockbuster success, but our small sites are serving their own communities well. We’re proud of you, and we want you here.
What does this mean? If there's enough moderation for a public beta site to consistently remain free of spam, for flags to be cleared, and for our Be Nice policy to be upheld, your site will remain open. However, if community leaders drop off, flags sit without being addressed, and we can’t find any suitable volunteers to step forward, the site gets closed.
Our job, at this point, is to keep our site filled with high quality posts. With that, we work on promoting it in whatever ways we decide are appropriate for the community. The combination of promoting the site and our continued involvement, will provide the useful Q&A site we are striving to be.
It's not always easy, but I don't see a reason to be discouraged about anything at this point. We have an active base to answer questions. We have an active base that is working behind the scenes on Meta to grow and guide the site. We have an active group of users in the chat room to discuss the site, life in general and my need for a very specific piece of hardware:
I'm looking for a piece of hardware that can torch leaves on the ground but not light my house or the trees on fire.