There are 2 things to confirm, which should allow the account to publish.
1. The account has publisher permission (or above)
2. If you look at the project permissions, confirm that the actual user permissions of the account itself has Save permission to the project.
It sounds like there is a conflict of permissions, by membership of different groups.
All the best
It have save permissions and for that particular group, user is member of only two groups, one grants viewer access and other publisher.
We know tableau promote roles not demotes so I do not find that a reason.
Thanks for looking into this.
Please show us a screen shot of the permissions for the specific Project. We should see the following:
1) Project level permission setting
2) Name of person who is having the issue
3) The user's actual permissions
On the user's end, you visually make sure they are logged on to the correct Tableau Server, to the correct Site, in the correct Project. We have seen before where the user mistakenly logs on to the wrong location so you need to verify this yourself visually, don't take the user's word for it. Make sure there are no duplicate names or similarly named objects e.g. "My Project" versus "My Projekt" or "My Projects". It happens.