It is possible to prevent users from disabling Outlook add-ins by using a GPO.  

Note: This article is about how to prevent users from disabling the add-in.  To prevent Outlook from disabling the add-in, see step #3 of this article.

  1. Open Group Policy and make sure that the Microsoft Outlook Administrative Templates are installed.  They are normally located under User Configuration...Administrative Templates...Microsoft Outlook (2013 or 2016).  If the Administrative Templates are not installed, you can download the templates from Microsoft here based on your outlook version:
    Office 2016:
    Office 2013:
    View this Microsoft article for help installing the template
  2. Click on the Miscellaneous folder on the left hand side.
  3. On the right hand panel, look for List of managed add-ins.
  4. Enable the List of managed add-ins policy.
  5. Write "SperrySoftwareEngine.Connect" and set the value to 1.  A value of 1 indicates that the add-in cannot be disabled by users.

That's it!

Alternatively, it's possible to deploy the registry key out via GPO.  The registry key type should be REG_SZ.