UPDATE

Released 15 Apr 2015

WORKAROUND

I use the Automattic iOS App 4.0.1

Over the weekend I noticed that the Preview option stopped working. Coincidentally (or was it? … Dunh dunh DAH), I got a warning saying that there was an Invalid Certificate problem with Contrafactual.com.

After several iterations I discovered the following:

Add a new site (your site as https://)
“Trust” the site when asked (twice)
As long as you don’t kill the app, the Preview option will work.
(The https:// version does not show up)
If you do kill it, just recreate the site.

I have commented on this issue here
http://ios.forums.wordpress.org/topic/getting-a-invalid-certificate-for-iphone-app?replies=26#post-11913

Here
http://ios.forums.wordpress.org/topic/preview?replies=9

Here
http://wpiphone.wordpress.com/2014/03/20/wordpress-for-ios-4-0-released/

And here
https://contrafactual.com/2014/04/07/debugging-test/

There is a definite relationship between the Certificate error and the Preview error.

Please, someone from WordPress, please investigate.

UPDATE

WP is aware of the issue and will fix in next release of the iOS app.

https://github.com/wordpress-mobile/WordPress-iOS/issues/1520