The entire situation regarding James and Louise Windsor's titles are ambiguous.
On the one hand, the Queen formally amended the LP of 1917 to exclude former wives, other than widows until they remarry, from using the style and title of HRH. The amendment included the former wives of the sons of the Sovereign, the former wives of the grandsons of the Sovereign, and the former wife of the eldest living son of the eldest grandson of the Sovereign. So the LP she issued covers every divorced wife of male members of the royal family entitled to use HRH under the LP of 1917.
On the other hand, there is no known formal LP or amendment that granted the style and title of Princess, to the former Lady Alice Montagu-Douglas-Scott, widowed Duchess of Gloucester. The Court Circular refers to her as "Princess Alice Duchess of Gloucester" starting on 13 July 1974, however; there is no grant of the style recorded at the College of Arms either. Alice received a grant of arms in 1981, in which the Queen sent a letter to the College of Arms specifically referring to her as "HRH Princess Alice, Duchess of Gloucester". Her Majesty approved armorial bearings that are those of HRH the late duke of Gloucester impaling the paternal arms of Her Royal Highness as previously depicted in the marital arms.
Then you have precedent.. In 1919, King George V issued an amendment to the LP of 1917 for the style and title of HRH Princess Victoria Patricia Helen Elizabeth, formally removing her HRH upon her marriage to the Honourable Alexander Ramsay. After marriage, she was to be known as Lady Patricia Ramsay. The change was effected at her own request, and George V commanded that the change also be recorded at the College of Arms, otherwise the LP amendment was null and void.
So you have two different and equally valid arguments regarding the Wessex children.
Royal styles and titles are a matter of the Sovereign's perogative, and are not subject to the laws of government. This means that the Queen's will and pleasure are all that matters, and she can change styles and titles as she pleases. Current thought is that how this is publicized makes no difference - whether it be by LP, press release, royal warrant or verbally.
But the precedent has been set that removing an HRH from persons entitled to use it, requires an amendment to the LP of 1917. We see it in the amendments made for the Duke of Windsor, Lady Patricia Ramsay, and the divorced wives of the House of Windsor.
Since there have been no LPs issued specifically removing the HRH from the Wessex children, I would say that they still retain the right to use it, if they choose to do so. Legally, they should still be HRH, regardless of whether they are called something different. And indeed, they are referred to in several instances as "Viscount Severn (legally HRH Prince James of Wessex)" and "The Lady Louise Windsor (legally HRH Princess Louise of Wessex)".
It has much the same overtones as Camilla being legally HRH The Princess of Wales, but using HRH The Duchess of Cornwall instead.
I can see both sides of this argument, but only time will tell the truth of the matter. If either Louise or James eventually use HRH then we'll have our answer.. but I don't see why they would, given that the HRH ends with them anyway in that branch of the family.