If the connector is running on top of CDP, you can check the log files under /var/log/kafka or /run/cloudera-scm-agent/process/xxxxxxxx-kafka-KAFKA_CONNECT/logs
If this is standalone kafka connect and no details in any log file, I would suggest adding the below JVM property to the process:
-XX:ErrorFile=targetDir/hs_err_pid_%p.log
The above property is to create a file when the JVM crash, when this happens no details are added to the log files.
Hope that helps to find the root cause.