My team has run into this Connect bug regularly in the last six months while doing infrastructure maintenance that causes intermittent broker availability issues. I'm a little surprised it exists given how routinely it affects us, so perhaps someone in the know can point out if our setup is somehow just incorrect. My team is running 2.0.0 on both the broker and client, though from what I can tell from reading the code, the issue continues to exist through 2.2; at least, I was able to write a failing unit test that I believe reproduces it.
When a KafkaBasedLog worker thread in the Connect runtime calls readLogToEnd and brokers are unavailable, the TimeoutException from the consumer endOffsets call is uncaught all the way up to the top level catch (Throwable t), effectively killing the thread until restarting Connect. The result is Connect stops functioning entirely, with no indication except for that log line - tasks still show as running.
The proposed fix is to simply catch and log the TimeoutException, allowing the worker thread to retry forever.
Alternatively, perhaps there is not an expectation that Connect should be able to recover following broker unavailability, though that would be disappointing. I would at least hope hope for a louder failure then the single ERROR log.