There was excaltly similar case which was closed:

https://issues.jenkins-ci.org/browse/JENKINS-56855

But this still happens with versions mentioned that issue.. Only way to resolve this was to restart the jenkins and the emails started to work again..  It might take up to 1-2 months before facing this again.

With debug logs I only see these:

Analyzing: ext-xxxx.yyyyyy@xxxx.fiAnalyzing: ext-xxxx.yyyyyy@xxxx.fiLooking for: ext-xxxx.yyyyyy@xxxx.fi starting at: 0 firstFoundIdx: 0 firstFoundIdx-substring: ext-xxxx.yyyyyy@xxxx.fi => found type: 0Analyzing: ext-xxxx.yyyyyy@xxxx.fiLooking for: ext-xxxx.yyyyyy@xxxx.fi starting at: 0 firstFoundIdx: 0 firstFoundIdx-substring: ext-xxxx.yyyyyy@xxxx.fi => found type: 0Analyzing: ext-xxxx.yyyyyy@xxxx.fiLooking for: ext-xxxx.yyyyyy@xxxx.fi starting at: 0 firstFoundIdx: 0 firstFoundIdx-substring: ext-xxxx.yyyyyy@xxxx.fi => found type: 0Adding recipients from trigger recipient listAnalyzing: jenkins@xxxx.fiLooking for: jenkins@xxxx.fi starting at: 0 firstFoundIdx: 0 firstFoundIdx-substring: jenkins@xxxx.fi => found type: 0Analyzing: jenkins@xxxx.fiLooking for: jenkins@xxxx.fi starting at: 0 firstFoundIdx: 0 firstFoundIdx-substring: jenkins@xxxx.fi => found type: 0Setting In-Reply-To since last build was not successfulSuccessfully created MimeMessageSending email to: ext-xxxx.yyyyyy@xxxx.fiMessagingException message: IOException while sending messageFinished: FAILURE