Use internet.nl to check your email settings. Get a 100% score.
They are a bit too harsh. You don't need 100%. Because they are checking things like DANE can only be achieved by customisation in DA if I'm correct. That's not pretty easy. And internet.nl substracts points for that.
78% is a nice score and this is because I don't have DANE and no RPKI. And for RPKI you can do nothing either. Datacenter needs to fix that. I've already asked Hetzner and they refuse to do that, because their own RPKI is in good order according to them.
And this is with DNSSEC enabled, which is also not really required for correct mail delivery. So without DNSSEC the score will even be lower.
So that's already reasons you will not pretty easy be able to achieve a 100% score. A 70+ score is well enough if the most important things are ok.
@DavidJB I would first check the Exim logfiles as also attachments can be wiped by the system due to the /etc/system_filter.exim file. I've customized that one.
Check with mail-tester.com because there you should have a 10/10 score without attachments anyway. If you don't have a 10/10, then something is already not in perfect order, things which -can- easily be made in perfect order.
Presuming you're using your own mailserver and not a 3rd party.
Another way is to send a fake invoice to my address, which is also set quite strict, if I don't receive it either then maybe I can see in the logs what is happening. But tray mail-tester.com first anyway.