Cause: When publishing is turned on, the subsite inherits the master page from the top level site. This overrides the theme. The subsite is set to inherit. The subsite is stuck with the master page and the theme is rendered unchangeable.
Solution:
- Open site in SharePoint Designer and open the Catalogues > Master page section in the folder list.
- Right click on the master page that you want to inherit from the main site (it will probably be default.master)
- Select Set as Default Master Page
- If you recieve a warning message, click OK
- Navigate back to the site and refresh the page
- Go to your Site Settings page and choose a new theme. Click OK
- Navigate back to your page and refresh.
NOTE: If you have turned off publishing, you will need to turn it back on for the changes to take place. If you have turned it off before step 1 above, you will not get any result after completing step 7.