As said by SaptakS, I applied the word-break to the message-Class. Since this breaks the line for long words without Spaces, as well as longer sentences, this is the better solution.
Since the max-width now is redundant, it got removed again, as to not cause any future confusion.
Too long single-line messages can cause the ChatUser-Panel to disappear.
Allowing the windows of the Chat to be only 80% of width will cause a automatic linebreak in such a case.