Personally, I must say that I have never understood why one would have a different capitalisation depending on the form of the text. Why should ‘Du’ be capitalised in a letter but not, say, in a dialogue of a novel? If it is considered a thing of respect then why wouldn’t the characters in a book be respectful to each other as well?
It is easy with ‘Sie’, of course: The word is capitalised every time it is used. It does not depend on context or whether it was written down using a pencil or a computer keyboard. It conveys its respectful meaning everywhere.
(That is, if the capital ‘S’ really is the sign of respectfulness and not simply a sign which says ‘I’m really not the third person plural “sie” but the version of it which describes a second person (singular or plural) but which looks and inflects just like the third person plural pronoun.’ – This argumentation might be more obvious if one thinks of the Pluralis Majestatis which attaches a singular meaning to plural form pronouns by – exactly – capitalising its initial letter. Obviously, following that argumentation makes no sense for the inherently singular ‘du’.)
So, if anybody wants to use ‘Du’ with a capital ‘D’, I think the writer should be consequent enough to really use it universally. (Of course, I do not know a single book where someone has followed this argumentation, so it is rather unorthodox.)