Do journals need to save all publication-relevant communications The journals I am talking about are those accepted by Scopus etc, Elsevier journals for example. 

From my personal morals, I consider it my right as an author after a submission to a journal to have full access to:


all my submitted documents during the review process
all reviewers' comments made, expect the confidential ones between editor and reviewer 
all additional editors comments
obviously during review but also afterwards, no matter whether the final result is an "accepted" or "rejected" paper


Now do such mandatory guidelines exist from the Scopus or CrossRef side? If not, are there publishers guaranteeing this? Email communications can be lost for various reasons like switching the university. This is somehow the case with me and I really would like to get access to comments from two years ago.
Journals do not have any legal obligation to store all documents associated with the review process. While many do store them in the electronic system, these systems are still relatively new. I have never heard discussions about record archiving polocies. Further, when journals switch review systems, the records are sometimes lost.

Of course, you have access to all these documents, and should use whatever archiving policy you think is relevant. I tend to save all the documents. I have paper files for my older manuscripts and purely electronic files for newer manuscripts.