This thread is resolved. Here is a description of the problem and solution.
Problem: "Sorry, you are not allowed to preview drafts." Solution: https://wpml.org/forums/topic/bug-impossible-to-preview-posts-written-in-default-language-on-other-domain/#post-1548101
Solution: Disabling "Auto sign-in and sign-out users from all domains" from WPML -> Languages resolved the issue.
I've checked your site and this option seems to be active.
There is a possible explanation behind this: https://wpml.org/forums/topic/cant-preview-changes-on-second-domain/#post-3346141
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