General Info for future reference:
BPS Pro versions affected: 12/12.1/12.2
WP Versions affected: WP versions below 4.6
Problem Scenario: Updates page: update-core.php > Update Plugins button: Bulk Plugin Update and Update Themes button: Bulk Theme Update. Performing a Plugin or Theme Bulk update on the WordPress Updates page: AutoRestore (ARQ) Automatic Shutdown & Backup Notice displayed and ARQ Bulk Update trigger was not turning ARQ Off.
Solution: Upgrade to BPS Pro 12.3.
Notes: WP 4.6 is scheduled to be released on August 16, 2016. BPS Pro 12+ uses ARQ AJAX Automation for WP 4.6+ versions. The BPS Pro 12.3 fix for the Plugin or Theme Bulk Update only applies to WP versions below 4.6. BPS Pro 12+ ARQ Automation is conditional based on the WP version that is installed (forward|backward compatibility).