CI_DB_driver Bug?

Again, quoting that same manual:

You are using a Windows client and the server had dropped the connection (probably because wait_timeout expired) before the command was issued.

The problem on Windows is that in some cases MySQL does not get an error from the OS when writing to the TCP/IP connection to the server, but instead gets the error when trying to read the answer from the connection.

... you should've really read it yourself.

A persistent connection may decrease your page load time on your local setup, but that's because it's only you using the application. When deployed on production, with pconnect set to TRUE, each time you have more than 1 visitor at a time, the second (and third, fourth, etc.) will have to wait for the first person's request to be fulfilled before they can load a page.

pconnect is not a magic "improve my performance" switch. It has a specific purpose and comes with certain implications that are now the reason for your issue. Just turn it off.