Assuming that your setting of <max_recovery_length> was left as the default, we suggested to increase it to 5000.
Since it was already 5000, then try 15000.
The aim is to see if the recovery capabilities of Lightstreamer can be increased, so that when you currently see "Insufficient data for recovery" you can see a successful recovery.
This is related to what you wrote: "recently after i increased the size of the message sent by the adapter". If the messages in transit are now big, the amount of data that should be kept to ensure recovery should be determined accordingly.
The hope is then that successful recovery from temporary outages can change the client experience significantly.

About the cause of the communication outages, for now there is no evidence that it can be caused by a Lightstreamer malfunctioning.
The Server log sent is very short (300 ms of activity), yet it shows normal activity on various sessions.
So, the interruption on a single session seems a client connectivity issue.
Only if you notice that many clients experience problems at the same time can we suspect a Server or local network problem.

For a preliminary check, you can send us a log of the Internal Monitor.
Please set the LightstreamerMonitorText logger at TRACE level in lightstreamer_log_conf.xml and send us the log produced in a few hours. But please, for now, take care of extracting only the log produced by this logger, otherwise the log could be very long.
With the current settings, you should grep for the "streamerMonitorText" pattern.