BrettEllis_CPM on ""MySQL server has gone away" during plugin upgrade"

About once a month, during which there are probably 15-30 plugin upgrades, I get the following server error:

PHP Waing: mysqli_query(): MySQL server has gone away in /blahblah/web/blog/wp-includes/wp-db.php on line 1811, referer: https://mysite.com/wp-admin/update-core.php?action=do-plugin-upgrade
This error message is immediately followed by:

mysqli_query(): Error reading result set's header in /blahblha/web/blog/wp-includes/wp-db.php on line 1811, referer: https://mysite.com/wp-admin/update-core.php?action=do-plugin-upgrade

From the user point of view, the plugin installation takes a long time, before getting the error.

I cannot correlate the error with anything - neither plugin nor date nor time nor...

In spite of the error, the plugin appears to have been successfully updated (I think), although I usually reinstall it, just in case. There is never such errors during reinstall.

If no one else knows right off the bat what might be causing this, can someone suggest a diagnostic technique that would allow me to focus better on what is going wrong?

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