Terraform Cloud will not show a new version of a private module when there is some kind of syntax error in the Terraform Configuration.
From the user's perspective, it may appear that the new module version is not published because of VCS issues or that the private module registry is not functioning properly.
To check the status of the latest version of the module you can go to the following link
https://app.terraform.io/app/<Organization>/registry/modules/private/<Organization>/<module name>/<provider>/status by substituting the <Organization>, <module name> and <provider> with the the values specific to your organization.
An easier way could be to open the module in Terraform Cloud and in the address bar of the browser to substitute the module's version with "status". That will lead you to a page similar to this:
There you can see a full error message that will help resolve the problem with the version publish.