Additional info posted (tracking for sanity): https://wordpress.org/support/topic/warning-error-while-sending-query-packet-pid82827?replies=30#post-8727317
Actually what makes more sense as the root cause of the problem is this:http://stackoverflow.com/questions/30753674/error-while-sending-query-packet
You guessed right MySQL have limitation for size of data, you need to break your query in small group of records or you can Change your max_allowed_packet by using SET GLOBAL max_allowed_packet=524288000;
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So here is the hypothetical scenario that appeared that uninstalling/reinstalling the plugin worked to fix the problem. The root cause of the issue/problem is the Data Type or the Data itself in a particular DB Table. For whatever odd reason or maybe just a coincidence or maybe an old problem with a particular DB table no longer exists after uninstalling/reinstalling the plugin. For that to be true the plugin would have to reusing or storing something that was previously part of the root problem, which actually has something to do with the Data Type or Data itself. So let’s say whatever the problem was that previously existed for a particular DB Table no longer exists and then you uninstall/reinstall the plugin and whatever old stored data (setting) no longer exists in that plugin. Then when you reinstall the plugin and root problem Data Type or Data in a particular DB no longer exists then the root problem is gone and the plugin settings do not store that problem.
If nothing has changed in how the plugin does what is does then the error should still be occurring. So logically the root cause has to do with the DB itself or a particular DB Table/Type/Data or of course a DB config setting.
Another possible clue that I was looking at was maybe this has to do with SSL? I would be curious to know how many people have SSL websites that are experiencing this particular issue/problem/error.