Thank you for helping improve our knowledgebase by posting to the Forum. Will you please verify that the Allow Emails is selected and try the following...
Select the Task that the External User is a Resource on and from the Toolbar, select the Email drop down and then choose 'Send Update Request'. You can also send by using 'Email to Resource' (if user is a resource).
If the User still does not receive an email then have their Email Administrator whitelist clarizen.com so that the emails are allowed.
Also, if you go to Settings --> System Settings --> Organizations, Users, Licenses --> 7.25 Send user triggered emails on behalf of the user -- Is this item checked or unchecked?
If you have further issues with this, please open a ticket and we will investigate what the issue may be.