I use the Energy Saver Systems Preference Schedule item to wake up the computer (in the wee hours) so a scheduled backup will run. If the computer is shut down and/or restarted, that seems to get suppressed. It still shows in the panel but doesn’t actually work (backups didn’t run). I un-check and then re-check the “Start up or wake” item and that seems to get things working again.
To avoid having to remember this, one can create an Applescript app (which runs a one-line Bash script) place it in one’s Login Items folder, but only if one has sudo priveleges. The Applescript is
do shell script "/bin/bash -c echo 'YourPassword' | sudo -S pmset repeat wakeorpoweron MTWRFSU 01:01:00"
Since your password is in the script, it’s wise to make it read-execute permission for its owner and no other privileges. It still may be a security risk, per