How to keep a dead mail account in Thunderbird

Question

I run 20+ different accounts on Thunderbird for work. One of our commercial providers has just stopped service. So every time I run "Get All New Messages", I get an annoying pop-up warning "Failed to connect to server ...".

I need to keep all historical mails which came and went via that server. I cannot have them in some obscure backup-archive, I need them inside my live Thunderbird, so that I can search, read, quote-from and forward those messages.

How can I disactivate this specific account, while still keeping all messages please? I tried in Account Settings to remove the entry for the server name, but Thunderbird does not accept an empty entry.

I have a hunch that there is a not-too-hacky way to keep an account present but dormant: There is one box in Account Settings > Server Settings > Advanced Account Settings which is labelled "Include this server when getting new mail". In my case for this account it is ticked, but grayed out. I guess if I could untick, then my question would be answered. Why is it grayed out and what do I need to change to make this option available?

Since that server has been turned off, I am reluctant to try my own experiments on my account settings, because there is no obvious way to recover those specific mails. Full backup does exist but is over 6 GB and would take forever...