Style tags cannot be saved in message templates and have in fact been stripped from current templates. We use a number of templates based on the Single Column Responsive Sample Template. In the last month, all the templates that used to contain a style tag that made the templates responsive have been stripped from the templates, including the sample template. Any attempts to re-add the style tag (or any style tag at all) seem to save fine, but on viewing do not have the style tag. Other changes are saved properly. I think this is since upgrading to 4.6.22, but am not sure of this.
Style tags can still be saved in CiviMail directly, just not in the templates.
CiviCRM 4.6.22 & Drupal 7.50