That I do not use anacron (and many don’t, remember that you have to install it extra) isn’t something to wonder. Apparently I have no use for it.
But I see your case.
I installed anacron on a 13.2 test system, to be able to read it’s man page.
My strong impression is that it is something for the system level. There are no end-user possibilities (not even the user functionality available in the system crontabs).
Now the above question is not covered by this thread’s title. Thus when you want a broader audience to discuss solutions, start a new thread with a title like:
“How to be sure that user cron jobs later when the system was down”
(well, invent your own title :)).
I could suggest something like a KDE command to start on login. That command (a script of course) could then test how long ago a backup was made and act accordingly. And of course it should update the timestamp. This requires to login on a regular base. But from your original question I assume that you do not want to logoutlogin, but to hibernate/resume. I would say loging out at least once a day is not a bad habit. An alternative could be a cron job that does run the sript every hour (xample, does not realy take much resources). Test the timestamp and it will bail out then most of the times. Just suggestions.
Ok, I’ll discuss this question properly in its proper thread. For the moment I’m fine using anacron by calling it in .profile and adding each job individually to anacrontab (because run-crons unnecessarily(?!) requires root permissions).