The King declared at his accession council that his brother was created a Royal Duke and would be styled "HRH The Duke of Windsor", so he remained HRH upon abdicating the throne at the will of The Sovereign.
I suppose it depends on whether you consider that the new king's mere declaration before the Privy Council on 12 December 1936, "My first act on succeeding My Brother will be to confer on Him a Dukedom and He will henceforth be known as His Royal Highness The Duke of Windsor", was enough to make him The Duke of Windsor, and a Royal Duke at that, or whether it was not effective until the Letters Patent were signed on 8 March 1937. I have not been able to find a copy of those Letters Patent, but it seems nothing about a Royal Style for David was actually put in writing until May 1937.
The abdication crisis raised the issue of whether David retained his HRH status, held by virtue of the 1917 Letters Patent, after the abdication, or whether by abdicating, and thus removing himself from the line of succession, he lost the right to be HRH. I suspect that as at December 1936 it was still generally considered that David retained his HRH status.
It was subsequently argued, and became the preferred interpretation, that the HRH style should only be held by people in the line of succession. This, of course, raises the interesting question of the status of HRHs who become Catholics.
The 1937 Letters Patent did not reconfer royal rank upon The Duke. It simply affirmed he would continue to hold it, notwithstanding the Abdication, but such attribute would be limited to him alone and could not be shared by his wife or future children.
I argue that the second 1937 Letters Patent actually conferred royal rank, on the basis that it had to be done because by then TPTB had decided that the most desirable outcome was for David to be held to have given up his right to be a RH by abdicating, and that the grant of it was to be a personal grant to him by his brother, unrelated to the 1917 Letters Patent, and also to remove any doubt concerning whether or not the effect of the March Letters Patent would have been that Wallis would become HRH on their marriage. I think this is confirmed in the undated draft letter from George to Edward, the final form of which was sent out on about 27 May 1937, which is included in the documents from the National Archives relating to the drafting of the Letters Patent which can be found here:
The drafting of the letters patent of 1937 :
Undated draft of a letter from the King to the Duke of Windsor
I feel bound to write to you about a matter which has been giving me great trouble and concern. All sorts of people, both official and private persons, are asking whether, when you marry, your wife will be made a "Royal Highness". It has never happened in all history that a woman who married a man who cannot succeed to the Throne has been so described; indeed, it is pointed out to me that, strictly speaking, you yourself lost the right to this title by the fact of abdication. As long ago as the time of Queen Victoria it was laid down that no one could be a "Royal Highness" who was not in the line of succession.
Now, as you can well believe, I don't want to do anything which would interfere with the continuance of your right to the title though, in order to secure it for you, I am advised that I ought to issue Letters Patent declaring that notwithstanding Queen Victoria's rule etc. you, as my brother and as former occupant of the Throne, are by my express direction to be so styled.
This must be strictly personal to you for the reason that a lady marrying outside the Royal Succession is never so styled and of course the same would apply to any children of the marriage. But I want you to understand that a great deal of trouble has been taken about all this and, apart altogether from the views of the lawyers, there is a great deal of concern that the situation should be made plain before your wedding. The Dominion Prime Ministers, who are here at the Imperial Conference, have been informally consulted and they all take the strongest view that what I am now advised to do is the proper course and that this is the only way to remove misunderstanding and heartburning hereafter. The necessary document will be issued later in the week but I am sending you this personal letter at once because of course I want you to understand that I have thought of this matter over from every point of view and I am satisfied that what has been decided is in the best interests of everybody, not forgetting your own future happiness.
Those documents from the Archives are fascinating. They include a note by Geoffrey Ellis, MP, Counsel to the Crown in Peerage and Honours claims from 1922 to 1954, in which he says, "Here, possibly, the question becomes one of political expediency in relation to general convenience and public opinion; and, therefore, within the province of the Prime Minister to advise the Crown what course may best be taken, rather than by seeking to extract from the law something it does not hold." I think that sums up the approach taken at the time. There was no precedent and those advising HM seem to have decided the outcome they wanted and worked out the way to achieve it. It seems clear that Bertie and Elizabeth and Mary all had a lot of influence on the approach taken regarding David and Wallis, for personal reasons. The more I read about this, the more I understand why David was so very, very angry about the way he was treated, and why he insisted that Wallis was styled HRH in France.