You can't directly invite people to join forever.
You will either run out of time or contacts. Perhaps worse, you'll upset your contacts with repeated requests to join the community).
This means, you need to encourage growth from existing members. You need to penetrate through the existing connections of your target audience. Academics call this the diffusion model of growth. Every member is a node, the message flows through the network until most of the nodes have turned purple. There are a lot of great strategies to boost word-of-mouth.
But what happens when this source of growth declines? This is where it gets interesting.
Growth can slow for two reasons.
1) Most members with an interest in that topic have already joined.
2) Most members within those pre-existing connections have already been reached.
If it's the former, that's fine. You've won. Congratulations, you've created the perfect community. Optimize your conversion ratio, work on your big wins, move to the mitosis phase and try to become self-sustaining. If you want to growth further, you need to create entirely new communities. That's your source of long-term growth.
If it's the latter, then you've hit a self-induced wall. You've only reached out to a single network of people, now most of them have joined. You need to use promotional tactics to reach new segments of your audience not connected to existing members.
This is the key point here. As your community moves into the maturity phase, you need a combination of word-of-mouth AND promotion to optimize growth
The focus will still be on word-of-mouth, but intense periods of promotion targeted at those outside of your current audience's demographics, habits, or psychographics will ensure you didn't miss potential members.