Alastair (shown right when Earl of MacDuff as heir to his Mother's title) was the only child of HRH Prince Arthur of Connaught and, in her own right, HH Princess Alexandra, 2nd Duchess of Fife, but usually called HRH Princess Arthur of Connaught after her marriage. He was a great-grandson of Queen Victoria, as his paternal Grandfather was the Queen's second son, Arthur, and also her great-great-grandson through his maternal Grandmother who was HRH Princess Louise, Princess Royal, the eldest daughter of HM King Edward VII. Not only did he have this distinction of birth and heritage, he was the only male of his generation who fell outside the remit of Letters Patent of 1917 which, further to changing the name of the Dynasty of the British Royal Family and dropping German titles almost exactly 100 years ago, meant a restriction of royal styles and titles in a streamlining of the descendants of Queen Victoria.
Below is his actual Birth Certificate which shows even his gender as 'Prince'!
In Letters Patent dated November 20, 1917, The King undertook further restructuring of the royal styles and titles by restricting the titles of Prince or Princess and the style of Royal Highness to the children of the sovereign, the children of the sovereign's sons, and the eldest living son of the eldest son of the Prince of Wales. This excluded Alastair, who was only a great-grandson of a sovereign (and was not the eldest living son of the eldest son of the Prince of Wales). It further stated that all titles of "the grandchildren of the sons of any such Sovereign in the direct male line (save only the eldest living son of the eldest son of the Prince of Wales) shall have the style and title enjoyed by the children of Dukes". Alastair, no longer considered a prince and the style of Highness (as opposed to Royal Highness) having effectively been abolished, now solely used his Mother's courtesy title, Earl of Macduff as heir to the Dukedom of Fife.
There is evidence of letters passing between various ministers, secretaries and the College of Arms with specific references to Alastair's style and title but this all appears to have been abandonned in favour of the above. Relatives of the generation above, even such as his own Mother and Aunt (but also the two Princesses Helena Victoria and Marie Louise, daughters of Princess Helena) had had their title, style and status confirmed by Warrant. As a toddler, Alastair hadn't and no action was taken further to just the proposal stage before the November Letters Patent came into effect.
As mentioned, Alastair was the only male of his generation who fell outside the remit of these Letters Patent. Queen Victoria had four sons: Albert Edward (Prince of Wales and eventually HM King Edward VII), Alfred (Duke of Edinburgh), Arthur (Duke of Connaught and Strathearn, and Alastair's Grandfather) and Leopold (Duke of Albany). Obviously, the eldest son and his immediate descendants were covered by the Letters Patent. Alfred and Leopold both only had one son each. Alfred and, in turn because Alfred's only son died before him without issue, Leopold's posthumous son Charles Edward both took up the Saxe Coburg inheritance and became a foreign Royal Duke. (Arthur renounced this inheritance for himself and his descendants.)
Not only did Alastair have the indignity of seemingly being forgotten as far as his royal status was concerned, he was not thought of as being particularly effectual. Maybe expectations were too high for his lack of a royal role and he simply fell by the wayside. The old Duke of Connaught certainly found his grandson's approach to his soldiering as hardly thorough.
Alastair's Father, Prince Arthur of Connaught, died of stomach cancer at age 55 on 12th September 1938 and the old Duke passed away on 26 January 1942. This meant that Alastair became the 2nd Duke of Connaught and Strathearn. Sadly, the new Duke enjoyed his new position and honours for little over a year before his own death in Ottawa whilst on "active service" on 26 April 1943. He had been assigned to Ottawa in 1939 as aide-de-camp to his distant relative the Earl of Athlone (HM Queen Mary's brother and husband to Alastair's cousin Princess Alice of Albany), then Governor General of Canada. Possibly his most onerous task had been to prepare the drinks tray even though he was allegedly fond of a whisky or two himself. Either way, Alastair's relatively short life came to an end when he supposedly died of hypothermia on his bedroom floor having opened the windows one freezing cold night in a drunken stupor.
His Grandmother's Marital Arms as Princess Royal and Duchess of Fife and his Mother's Coat of Arms as Duchess of Fife in her own right are shown below.
Unfortunately, as with most of his life, he wasn't anything effectual - whether Prince or Duke - for long enough for a decision to be taken. Sadly, it doesn't strike me that anyone was particularly bothered with him in any aspect of his life and his own attitude and failings certainly didn't help.
From almost every viewpoint, Alastair was quite simply an anomaly...