So by upgrading the input plugin you fixed the keep-alive issue that causes the connection between beats and Logstash to be closed. But you still need to address the underlying issue in Logstash which is most likely some form of back-pressure (either a blocked/slow output, a poor performing logstash filter).
If you haven't checked the Logstash logs do that first.
Then take a look at the node stats for the instance. Perhaps you will spot a section in the pipeline that's taking lot's of time or has errors.
Another tool is the pipeline viewier which gives you a visualization of the pipeline with metrics about each stage.