I've never used Mac Mail properly myself as I only have a windows PC. @BillC45 has pointed out to other users, Apple devices seem to have a habit of mysteriously deleting emails. I sometimes feel I should invest in a Mac to see what's going on.
However first thoughts:
The setting to automatically expunge deleted mails in your Mac has been changed. This means that mails are marked for deletion but not actually deleted but are hidden from you unless in Mac Mail.
I would certainly look at the advice in the link about changing filters in Mac Mail itself. While common sense would suggest it shouldn't be involved in these deletions, it wouldn't be the first time I've seen unexpected behaviour in mail clients.
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Something is adrift with that account. I did set up 'autoforwarding' as per those previous suggestions, but it doesn't work. Although some emails have got through to my iPad (more so than my Mac), they have come through on the standard address, not the autoforward address.
I think it'll be easier to abandon that address, and switch to another more reliable one. I do find that the @yahoo.com addresses are 'better', although not quite as speedy as @ntlworld ones - the only reason I set up some yahoo mails was security. I got fed up with being restricted to the ten-character password limit imposed here at Virgin.
But having lived a long time, when I find a brick wall, I am no longer inclined to bash my head against it!
Apple/Mac Mail has a long history of “mysterious” problems which result in some users losing some, or even all, of their mails. Apple Mail is now more or less the same product across all Apple platforms. However, I think that a key problem with Apple Mail is that it seems to acquire more options – and thus complexity – every year. Put this on top of the complexities of IMAP and the average consumer will struggle to keep up. I note that you have not previously encountered the “email with a strikethrough” - which means that – one email client on an IMAP-connected device has flagged that email for deletion – but the Trash folder hasn’t been emptied yet, so it remains visible on the host website until then. Note that if you have any sort of automatic filter set up on mail to delete certain incoming emails, a “strikethrough” email may well appear in your Inbox without you ever having clapped eyes on it previously.
Have a look at this thread where I attempted to quantify the incidence of the “disappearing” problem in the context of the number of iphones sold in 2017 alone (216 Million).
I'll keep a close eye, but it really does appear to be only one of my @ntlworld.com addresses (I have three) that is misbehaving. Perhaps the address itself has acquired some sort of corruption over the years.
I'll gradually withdraw from that address, and lean more towards @yahoo, which gives me that big password security (yes, I know that Yahoo too can get hacked!).
I have tried one or two other mail programs as alternatives to Mail (Mac), but there's always something that doesn't suit me (old age).
Now, if only the four of us were running an email service, we might get it right, no?