Some emails arrive, some do not

If the sender received a bounce message, read the possible causes.

If they did not receive a bounce message and some of their messages arrive, whilst others don’t, possible causes are as follows.

MX records may list other servers – only our MX servers should be listed.
The sender may send from multiple servers – one of those servers could be blacklisted, whilst the others are OK – therefore some emails will arrive and some will be blocked.
This would be the same if the sender is sending some emails from their website or a third party newsletter system – it’s quite common for web servers to be blacklisted, even though the main email server is not.
The sender is triggering spam filtering rules – check your junk folder and email quarantine (although if an email was quarantined, it’s almost certain that the sender received a bounce back saying that the email wasn’t delivered).