javax.mail.MessagingException when using the Log4J SMTPAppender in EAP 6

Issue

I have the Log4J SMTPAppender installed as a custom handler in EAP 6. Every once in a while I get an exception like this in the log:

log4j:ERROR Error occured while sending e-mail notification.
javax.mail.MessagingException: Exception reading response;
  nested exception is:
        java.net.SocketException: Connection reset
        at com.sun.mail.smtp.SMTPTransport.readServerResponse(SMTPTransport.java:2210)
        at com.sun.mail.smtp.SMTPTransport.close(SMTPTransport.java:1222)
        at javax.mail.Transport.send0(Transport.java:197)
        at javax.mail.Transport.send(Transport.java:124)
        at org.apache.log4j.net.SMTPAppender.sendBuffer(SMTPAppender.java:416)
        at org.apache.log4j.net.SMTPAppender.append(SMTPAppender.java:256)
        at org.apache.log4j.AppenderSkeleton.doAppend(AppenderSkeleton.java:251)
        at org.jboss.as.logging.logmanager.Log4jAppenderHandler.doPublish(Log4jAppenderHandler.java:129)
        at org.jboss.logmanager.ExtHandler.publish(ExtHandler.java:76)
        at org.jboss.logmanager.LoggerNode.publish(LoggerNode.java:292)
        at org.jboss.logmanager.LoggerNode.publish(LoggerNode.java:300)
        at org.jboss.logmanager.LoggerNode.publish(LoggerNode.java:300)
        at org.jboss.logmanager.LoggerNode.publish(LoggerNode.java:300)
        at org.jboss.logmanager.LoggerNode.publish(LoggerNode.java:300)
        at org.jboss.logmanager.Logger.logRaw(Logger.java:721)
        at org.jboss.logmanager.Logger.log(Logger.java:672)
        at org.jboss.logging.JBossLogManagerLogger.doLogf(JBossLogManagerLogger.java:50)
        at org.jboss.logging.Logger.logf(Logger.java:2093)
        at org.jboss.as.jsf.JSFLogger_$logger.managedBeanLoadFail(JSFLogger_$logger.java:53)
        at org.jboss.as.jsf.deployment.JSFManagedBeanProcessor.deploy(JSFManagedBeanProcessor.java:105)
        at org.jboss.as.server.deployment.DeploymentUnitPhaseService.start(DeploymentUnitPhaseService.java:120)
        at org.jboss.msc.service.ServiceControllerImpl$StartTask.startService(ServiceControllerImpl.java:1811)
        at org.jboss.msc.service.ServiceControllerImpl$StartTask.run(ServiceControllerImpl.java:1746)
        at java.util.concurrent.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1145)
        at java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:615)
        at java.lang.Thread.run(Thread.java:724)
Caused by: java.net.SocketException: Connection reset
        at java.net.SocketInputStream.read(SocketInputStream.java:189)
        at java.net.SocketInputStream.read(SocketInputStream.java:121)
        at com.sun.mail.util.TraceInputStream.read(TraceInputStream.java:110)
        at java.io.BufferedInputStream.fill(BufferedInputStream.java:235)

This will happen after the thread has been hung for about a minute.