After months of speculation, Buckingham Palace confirmed Harry would attend the Coronation without Meghan Markle and the children, who would remain home in California.
Archie’s birthday falls on the same day as the Coronation, meaning Harry will miss his son’s celebrations.
Ms Griffiths said it would have been the “perfect opportunity” for some “special recognition”.
Writing for the Daily Mail she added: “Charles was said to be open to the suggestion that he should make a gracious nod to Archie and rumours circulated that he would raise a glass to his grandson during a post-procession Coronation lunch.”
However, a source said it is “unlikely” as “no member of the Sussex family” is due at the lunch.
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Last month the Royal Family website was updated after Meghan and Harry confirmed they had christened Lilibet.
Archie, three and Lilibet, one, were named as the Prince and Princess of Sussex on the line of succession page for the first time as sixth and seventh in line to the throne.
The siblings were previously listed as Master Archie and Miss Lilibet.
Under rules set out by King George V in 1917, Archie and Lilibet were not Prince and Princess at birth because they were not grandchildren of the monarch but gained the right to these titles when Charles acceded to the throne following the death of Queen Elizabeth II.
Announcing Harry’s attendance, Buckingham Palace said: “Buckingham Palace is pleased to confirm that the Duke of Sussex will attend the Coronation Service at Westminster Abbey on 6th May.
“The Duchess of Sussex will remain in California with Prince Archie and Princess Lilibet.”
While his attendance is confirmed, it is unclear the role he will play in proceedings.
Prince William who is heir to the throne will play a “significant” role, and his son, Prince George also playing a poignant role.
As one of the eight Pages of Honour George will form part of the procession through the Nave of Westminster Abbey.