If the background indexing fails for some reason it logs the exception for the first time then it logs the exception like The index update failed .... After that if indexing continues to fail then no further logging is done so as to avoid creating noise.
This poses a problem on long running system where original exception might not be noticed and index does not show updated result. For such cases we should expose the indexing health as part of IndexStatsMBean. Also we can provide the last recorded exception.
Administrator can then check for MBean and enable debug logs for further troubleshooting