Hi Daniel,
From my own experience, the one and only time we had similar issue (in test environment), the job generated by F110 was cancelled. There was clear message in job log stating what went wrong and it had nothing to do with email or no email in vendor master. You could search in SM37 with program name RFFOAVIS_FPAYM in your system within range of dates. Regardless whether your job is cancelled or not please read its log. It may shed some light.
Exception handling is defined in ABAP code in function module attached to BTE 2040, which is called by RFFOAVIS_FPAYM. The standard FM tries to send fax if no email is available.
We customized this code and send a CC of payment advice (using OSS 1033893 ) to AP department and therefore always have an email address coming out of FM attached to BTE 2040.
Please check in tcode FIBF, Settings, Process modules of ...Customer – which FM is assigned to 2040. If its name starts with Z* then check in the code of function module (SE37) what exactly it does in your system when no address could be selected.
Best regards,
Anton