I've been looking between questions, e.g. How to determine the close date of a closed beta site? However, it is not clear to me the procedure or the circumstances under which a beta site is closed.
However, it is not clear to me the procedure or the circumstances under which a beta site is closed.
Whether a Beta Site is closed or not appears to be at the sole discretion of Stack Exchange Inc. So there is no clear-cut reasons for why a site may be closed or not. However, there are factors which may help you in determining if a beta site has a better chance at being closed or graduated to a full site.
For example, you can click on the Beta Site you want, and see a breakdown of statistics. For example, here's Aviation :
Red is bad, orange is OK, and green is good.
The more red, the more likely a beta could be closed probably. The more green, the more likely a beta gets to be a graduated site probably.