Beta sites can be closed at any time when it's become clear that the beta won't produce a site that is contributing useful content at the appropriate level for SE. This is a decision made by the community team. Private betas are especially scrutinized for both quality and quantity, and won't be allowed to go public if they aren't up to par. In many cases the site may get an extended beta to try to work out the issues, but that didn't happen this time. Once a site is public, they're reluctant to close it until it's absolutely necessary, but it can still happen.
In the case of mental fitness, the site was lacking in both quality and quantity. There were a number of problems with the site, but the biggest one was that it didn't seem to have any community developing. Rather than duplicating what was already said on their meta site, I've screencapped it here. This wasn't exactly the first warning though; it was very clear from day 1 to most users and to the community managers that there were some big issues with the site that needed to be addressed.