"Lost connection to MySQL server" for various reasons

I know that upon first glance this might seem like a duplicate post. I can see there are various posts already published regarding this topic. However, all of those posts seem to be about very specific actions causing the users/admins to see the "Lost connection" errors. My situation seems a bit different as I'm not doing specific actions to generate these errors. I don't notice when they happen, because I don't check my PHP error logs very frequently (they're not errors that show up on the front-end or back-end of my sites; just in the error log). Here's a sample of the most recent errors I've found:

WordPress database error Lost connection to MySQL server during query for query SELECT option_value FROM wp_options WHERE option_name = 'et_pb_role_settings' LIMIT 1 made by include('phar:///opt/wp-cli/bin/wp/php/boot-phar.php'), include('phar:///opt/wp-cli/bin/wp/php/wp-cli.php'), WP_CLI\Runner->start, WP_CLI\Runner->load_    WordPress, require('wp-settings.php'), do_action('init'), WP_Hook->do_action, WP_Hook->apply_filters, call_user_func_array, et_setup_builder, require('/themes/Divi/includes/builder/framework.php'), et_builder_load_framework, et_builder_settings_init, ET_Builder_Settings::get_instance, ET_Builder_Settings->__construct, ET_Builder_Settings->_initialize, ET_Builder_Settings::_get_page_settings_fields, et_pb_is_allowed, et_pb_get_role_settings, get_option
WordPress database error Lost connection to MySQL server during query for query select count(*) from wp_cptch_track_countries  where name = 'Europe'  made by require('wp-blog-header.php'), require_once('wp-load.php'), require_once('wp-config.php'), require_once('wp-settings.php'), include_once('/plugins/captcha/captcha.php'), include_once('/plugins/captcha/hcptc-live-traffic.php'), cptch_create_db
WordPress database error Lost connection to MySQL server during query for query select count(*) from  wp_cptch_track_visitor where requested_url = 'http://'  made by include('phar:///opt/wp-cli/bin/wp/php/boot-phar.php'), include('phar:///opt/wp-cli/bin/wp/php/wp-cli.php'), WP_CLI\Runner->start, WP_CLI\Runner->load_    WordPress, require('wp-settings.php'), include_once('/plugins/captcha/captcha.php'), include_once('/plugins/captcha/hcptc-live-traffic.php'), cptch_add_visitor
WordPress database error Lost connection to MySQL server during query for query SELECT  t.*, tt.* FROM wp_terms AS t  INNER JOIN wp_term_taxonomy AS tt ON t.term_id = tt.term_id WHERE tt.taxonomy IN ('category') ORDER BY t.name ASC  made by do_action('admin_init'), WP_Hook->do_action, WP_Hook->apply_filters, call_user_func_array, ET_Dashboard->set_post_types, get_categories, get_terms, WP_Term_Query->query, WP_Term_Query->get_terms
WordPress database error Lost connection to MySQL server during query for query SHOW FULL COLUMNS FROM `wp_options` made by require('wp-blog-header.php'), require_once('wp-load.php'), require_once('wp-config.php'), require_once('wp-settings.php'), do_action('init'), WP_Hook->do_action, WP_Hook->apply_filters, call_user_func_array, wp_cron, spawn_cron, set_transient, update_option
WordPress database error Lost connection to MySQL server during query for query SELECT option_value FROM wp_options WHERE option_name = 'mwp_show_plugin_update' LIMIT 1 made by require_once('wp-load.php'), require_once('wp-config.php'), require_once('wp-settings.php'), include_once('/mu-plugins/0-worker.php'), include_once('/plugins/worker/init.php'), mwp_init, get_option
WordPress database error Lost connection to MySQL server during query for query SELECT option_value FROM wp_options WHERE option_name = 'endurance_user' LIMIT 1 made by require('wp-blog-header.php'), require_once('wp-load.php'), require_once('wp-config.php'), require_once('wp-settings.php'), include_once('/plugins/sumome/sumome.php'), WP_Plugin_SumoMe->__construct, get_option
WordPress database error Lost connection to MySQL server during query for query SELECT option_value FROM wp_options WHERE option_name = 'mwp_show_plugin_update' LIMIT 1 made by require('wp-blog-header.php'), require_once('wp-load.php'), require_once('wp-config.php'), require_once('wp-settings.php'), include_once('/mu-plugins/0-worker.php'), include_once('/plugins/worker/init.php'), mwp_init, get_option
WordPress database error Lost connection to MySQL server during query for query SELECT option_value FROM wp_options WHERE option_name = 'et_google_fonts_cache' LIMIT 1 made by require('wp-blog-header.php'), require_once('wp-includes/template-loader.php'), include('/themes/Divi/page.php'), get_header, locate_template, load_template, require_once('/themes/Divi/header.php'), wp_head, do_action('wp_head'), WP_Hook->do_action, WP_Hook->apply_filters, call_user_func_array, wp_enqueue_scripts, do_action('wp_enqueue_scripts'), WP_Hook->do_action, WP_Hook->apply_filters, call_user_func_array, et_divi_load_scripts_styles, et_builder_enqueue_font, et_builder_get_fonts, et_builder_get_google_fonts, get_option
WordPress database error Lost connection to MySQL server during query for query SELECT option_value FROM wp_options WHERE option_name = 'wpaas_toplevel_page_hidden_tabs' LIMIT 1 made by require('wp-blog-header.php'), require_once('wp-load.php'), require_once('wp-config.php'), require_once('wp-settings.php'), do_action('init'), WP_Hook->do_action, WP_Hook->apply_filters, call_user_func_array, WPaaS\Admin\Pages->init, get_option
WordPress database error Lost connection to MySQL server during query for query SELECT * FROM wp_bpspro_arq_exclude WHERE arq_exclude_source LIKE '%/%' made by include('phar:///opt/wp-cli/bin/wp/php/boot-phar.php'), include('phar:///opt/wp-cli/bin/wp/php/wp-cli.php'), WP_CLI\Runner->start, WP_CLI\Runner->_run_command, WP_CLI\Runner->run_command, WP_CLI\Dispatcher\Subcommand->invoke, call_user_func, WP_CLI\Dispatcher\CommandFactory::WP_CLI\Dispatcher\{closure}, call_user_func, Cron_Event_Command->run, Cron_Event_Command::run_event, do_action_ref_array, WP_Hook->do_action, WP_Hook->apply_filters, call_user_func_array, bps_Master_ARQ_Fire, bps_ARQ_wpincludes
WordPress database error Lost connection to MySQL server during query for query SELECT option_value FROM wp_options WHERE option_name = 'bulletproof_security_options_SLF' LIMIT 1 made by require_once('wp-load.php'), require_once('wp-config.php'), require_once('wp-settings.php'), include_once('/plugins/bulletproof-security/bulletproof-security.php'), require_once('/plugins/bulletproof-security/admin/includes/admin.php'), get_option
WordPress database error Lost connection to MySQL server during query for query UPDATE `wp_options` SET `option_value` = 'a:2:{s:14:\"bps_arq_status\";s:0:\"\";s:24:\"bps_arq_status_timestamp\";s:10:\"1515457835\";}' WHERE `option_name` = 'bulletproof_security_options_ARQ_status' made by include('/plugins/bulletproof-security/admin/wizard/wizard.php'), bpsSetupWizard, update_option
WordPress database error Lost connection to MySQL server during query for query SELECT * FROM wp_bpspro_arq_exclude WHERE arq_exclude_source LIKE '%/%' made by do_action_ref_array, WP_Hook->do_action, WP_Hook->apply_filters, call_user_func_array, bps_Master_ARQ_Fire, bps_ARQ_wpincludes
WordPress database error Lost connection to MySQL server during query for query UPDATE `wp_options` SET `option_value` = 'a:1:{s:22:\"bps_error_log_date_mod\";s:24:\"January 23 2018 00:49:09\";}' WHERE `option_name` = 'bulletproof_security_options_elog' made by require_once('wp-config.php'), require_once('wp-settings.php'), do_action('wp_loaded'), WP_Hook->do_action, WP_Hook->apply_filters, call_user_func_array, MWP_    WordPress_HookProxy->hook, call_user_func_array, MWP_Worker_Kernel->hookResponse, call_user_func, mmb_do_upgrade, MMB_Installer->do_upgrade, MMB_Installer->upgrade_plugins, Plugin_Upgrader->bulk_upgrade, WP_Upgrader->run, WP_Upgrader->install_package, apply_filters('upgrader_post_install'), WP_Hook->apply_filters, call_user_func_array, bpsPro_arq_automation_plugins_themes_post_install, update_option
WordPress database error Lost connection to MySQL server during query for query SHOW FULL COLUMNS FROM `wp_options` made by do_action('wp_ajax_update-plugin'), WP_Hook->do_action, WP_Hook->apply_filters, call_user_func_array, wp_ajax_update_plugin, Plugin_Upgrader->bulk_upgrade, WP_Upgrader->run, WP_Upgrader->install_package, apply_filters('upgrader_post_install'), WP_Hook->apply_filters, call_user_func_array, bpsPro_arq_automation_plugins_themes_post_install, update_option

Basically, I'm wondering if anyone can see what could be causing the lost connections. I'm not very familiar with PHP or PHP errors so I can't tell if these errors are cause for concern.

Thank you for any help/tips with this! I'm also very happy to provide more information about this!

~Jutta