Jenkins ver. 1.598
Debian Wheezy 32bit

Need a bit more information on this. How do you have your job configured? Which email plugin are you using (Mailer or email-ext)?

I'm sorry, I thought I did describe it better.

The mail server is configured as 'mygit' with 'mygit' in /etc/hosts as '1.2.3.4 mygit'.

The job is configured to send an email notification to 'proj_myapp' for every unstable build.
'proj_myapp' is an alias that is configured on 'mygit', and to which I can send email without problems.

Before this used to work just fine.
I don't know which version of Jenkins broke it since I don't regularly update Jenkins and don't have failing builds very often.

It still doesn't work for Jenkins 1.607.

Which mailer plugin are you using? Also, which version of Jenkins did it work on?

mailer = the default Jenkins mailer, currently @ 1.15

which version: (as I said) I don't know. probably a few versions before I filed the bug

Can you provide a config.xml for the job and a build log?

The xml I can only provide privately.
The part relevant to email:

    <hudson.tasks.Mailer plugin="mailer@1.12">
      <recipients>proj_nbsolsrd</recipients>
      <dontNotifyEveryUnstableBuild>false</dontNotifyEveryUnstableBuild>
      <sendToIndividuals>false</sendToIndividuals>
    </hudson.tasks.Mailer>

There is nothing special in the build logs.

Failed build:

Build step 'Execute shell' marked build as failure
Archiving artifacts
An attempt to send an e-mail to empty list of recipients, ignored.
Started calculate disk usage of build
Finished Calculation of disk usage of build in 0 seconds
Started calculate disk usage of workspace
Finished Calculation of disk usage of workspace in 0 seconds
Finished: FAILURE

Next successful build:

Archiving artifacts
An attempt to send an e-mail to empty list of recipients, ignored.
Started calculate disk usage of build
Finished Calculation of disk usage of build in 0 seconds
Started calculate disk usage of workspace
Finished Calculation of disk usage of workspace in 0 seconds
Finished: SUCCESS

My guess is that Mailer tries to resolve proj_nbsolsrd to a username, which is can't do and so it replaces it with an empty string. Can you try setting up a user in the Jenkins database with the username proj_nbsolsrd and specify the email address as proj_ngsolsrd and see if that works?