Problems with Mac Mail

I am experiencing problems with an IMAP email account in Mail on my MacBook Air.

At the end of 2020 I found (by checking my mail using my Android phone) that some emails were not downloading into Mail on the Apple laptop. The company which hosts my personal email account eventually advised me to delete the IMAP account from Mail and re-create it.

However, this did not solve the problem of a few missing emails. 

And it introduced a new one: the numerous emails in my Inbox and Sent mailboxes in Mail which were there prior to recreating the IMAP account vanished and did not reload.

Just to explain: I file all emails in a vast number of Mailboxes within Mail. The emails which vanished were ones I had not got round to filing (or deleting!)

Further investigation by the company hosting my email account revealed a possible explanation for the syncing failing. Apparently the email servers (which are based in the UK) were frequently shown that my devices (in fact I only have two devices – my MacBook Air laptop and an Android phone) are showing multiple concurrent IP connections. For security I believe that a finite number (I think 16 may have been mentioned) and that further connections are blocked.

I reported this to my broadband supplier (I am currently based in Malaysia). Their initial reaction was to say “you have a dynamic IP service”. My response was to say: “as I understand it, dynamic IP simply selects a fresh IP from time to time – IT SHOULD NOT KEEP THE PREVIOUS IP ADDRESSES OPEN. THIS – I BELIEVE – IS THE FALULT WHICH IS PREVENTING MY EMAIL SERVER IN THE UK COMMUNICATING CORRECTLY WITH THE EMAIL SOFTWARE ON MY LAPTOP.

This prompted  them to undertake further investigations. 

I am not sure what action (if any) they took to solve the problem but two weeks a footnote suddenly appeared below all the Mailboxes in Mail saying it was downloading over 1000 new messages!

I have had my laptop online, with Mail open for a few hours every day for two weeks. Genuinely new emails seem to come in UK.

BUT…the missing messages never arrive. 

After two weeks all that happens is that the footnote message keeps changing. Yesterday it said: “downloading messages: 59 of 3,246. Then it said “60 new messages; a litle late “68 new messages”. And today it said “Downloading Messages: 60 of 2,519” – which swiftly changed to “61 new messages”

But none of the missing emails have yet appeared anywhere Mail. I know, from checking webmail, that my Inbox is missing 769 mails and SENT is missing about 250 emails. Which makes the footnote communications even more confusing.

No-one seems to have any idea where all these messages which are  – apparently downloading – are going!

Can anyone throw light on what is going on?

My Mail software is version 11.5, which is, I believe, the most up-to-date version I can run on the laptop, which uses OS High Sierra, version 10.13.6, as its operating system.