It seems odd that email would stop working all of a sudden when it did work.  If you are not using credentials to your forwarder then it should work but as you indicate it is not.  Are you able to set up credentials and test them to see if that fixes it?

This is the email setup page from Veeam help - Configuring Global Email Notification Settings - User Guide for VMware vSphere (veeam.com)

The only other thing I can think of is the OS being Win2012R2 which is fairly old now.  The other servers that work are they the same or newer for OS?

maybe something you obviously already checked, windows updates?

As I said, the two VMs that no longer work (only in terms of sending mail, as the backup works perfectly), are under 2012R2.
The others are running under 2019 standard
But then, it's only sending mail, so I don't really see what's the problem.
Both 2012R2 servers are up to date.

and yes, I followed the instructions on this page https://helpcenter.veeam.com/docs/backup/vsphere/general_email_notifications.html?ver=120 perfectly, step by step.

sorry, what i meant was, are backup installed recently? Dit you try to re apply the email settings in configuration menu? 

Well then these should technically work and send email still.  I know you are using community edition, but might be best if you can contact Support to see what is happening.

Also try to apply the email settings again as noted by Epicfailing.

The servers did their backups this weekend, just that I no longer receive notifications of backups and configuration backups.
The VMs have now been installed for a little over 2 years, worked perfectly until about 3 weeks ago, and I updated them to the last version last week (thinking that would solve the problem).
I deactivated email sending, rebooted the vm and reactivated email sending, on the old version it worked randomly (and when it worked, the next day it didn't), on the new version it doesn't work at all.

Are you able to set up authentication with your email relay server to test that?  If not at this point support is the best bet to help resolve this.

You can also check the logs here to see if anything within there gives an idea as to what the issue is - C:\ProgramData\Veeam - unsure which log file has the email stuff but will check my servers and post back.

even if I have a community version, will the official veeam support take my request?

I've had a good look in the veeam logs and apart from the famous message ( Unable to connect to SMTP server because of invalid credentials or connection settings.), I don't have much more to give in the way of details, and yet I'm used to dissecting linux-type logs.

Yes you can submit a ticket for support but the response is best effort unfortunately.  You might also try to search the forums to see if there are any posts there that are helpful - https://forums.veeam.com

Thank you
I will contact them to see if they can help me.
Unfortunately I've already search in the official forum but haven't found anything.

I'll let you know if I find a solution.

Sounds good.  Keep us posted and I am sure if others have more details they will post here.