Can you share a few of the topic links from your notifications ?
If replies appear to be missing, a few possibilities (outside of technical glitches) are:
Posts have been deleted by the original author.
Posts have been flagged by community (usually temporarily hidden pending moderator review). This may result in off-topic posts being moved to a new topic and spam posts being deleted.
You should still have an option to see temporarily hidden posts, eg:
Perhaps some notifications you noticed were related to Likes, Accepted Solutions, Quotes, or Following activity rather than Replies. If you visit notification activity in your account (or by clicking on your user avatar at the top right of the page), each notification will be prefixed with an icon for the activity type.
The example below shows a favourite, a reply, and an accepted solution:
Replies can generate email notifications as they indicate something to read or respond to. I believe most other notifications (eg Likes or Quotes of your posts) are informational and will not trigger emails.
All notifications were showing “replied” status by OPs. Much later during the day, they got responses from OP and/or others. but it was “much” later, like 4-5 hours.