Pressable provides a weekly report of sites that need theme and plugin updates.
This is an opt-in feature, and can be enabled by an account owner here: https://my.pressable.com/settings/sites

Plugin and Theme Actions
Pressable enables you to manage your WordPress plugins and themes directly within the MyPressable Control Panel (MPCP). You can refresh the list, update, activate, and deactivate plugins and themes using this feature that’s accessible to all users.
Plugin Management
Pressable also provides a plugin management tool to help keep your sites updated. The plugin management functionality doesn’t work with some premium theme and plugins (due to licensing issues). The Plugin & Theme update report can work well to catch any premium products that may not have been updated by the plugin management functionality.