The reopening of application windows or documents is currently controlled by the operating system. There are two settings that control this behavior; one is in System Preferences, the other presents itself just prior to shutting down or restarting.
The system setting (which can be found by selecting Menu Bar ▸ ▸ System Preferences… ▸ General) controls whether app windows are reopened after quitting and relaunching an app. If you’d like OmniPlan to reopen documents that were left open the last time OmniPlan was quit, you’ll want to make sure that “Close windows when quitting an app” is unchecked.
The other setting (which presents itself when you either shutdown or restart your Mac) controls whether app windows are reopened after restarting the Mac. To control that, you’ll want to confirm that the checkbox next to “Reopen windows when logging back in” is checked on the “Are you sure you want to restart your computer now?” prompt.
As @ains mentioned above, we do have a feature request for controlling this specifically within OmniPlan. If using the available system settings doesn’t meet this need for you, we’d love to hear why via email so we can be sure to capture your thoughts in our request tracker.