The story is published, @name is visible in the caption, and the person got nothing. There are several causes and they are different in kind.
Offsets in the caption
A mention in Telegram is not the text «@name» — it is separate markup saying which character it starts at and how many characters it covers. Those characters are not counted the way a person counts them: one emoji takes two positions.
Hence the classic failure: an emoji is added to the caption, the markup shifts, and the mention now points at a neighbouring piece of text. The story publishes, no error appears, nobody is notified. If you write captions by hand, check on a second account after every edit.
Privacy settings
The subtler case: the notification arrives and the story does not. Indistinguishable from the outside — no replies either way. Explained separately.
The username is gone
Usernames get changed and released. A list built three months ago contains names behind which there is nobody — or somebody else. The second is worse: the mention goes to an unrelated person.
Lists for stories therefore need refreshing more often than lists for outreach. On ageing lists in general — dead entries.
The account is restricted
The worst case: stories still publish but reach fewer people and notifications partly stop. No explicit error appears. Signs and remedies — story limits.
How Neurogram does this
Everything above is manual work that runs into the number of hours in a day. Neurogram does it on your own accounts and without you: it collects channels and audiences, writes comments and replies with a language model, and keeps limits and quiet hours so the accounts survive. See pricing or look at your case.