There is no evidence that the Empire and the First Order aren't backing up their information.
The Imperials were not after the stolen Death Star plans because they needed them for their own use. They were concerned with the Rebels utilizing the plans to find a weakness in the battle station.
From the ANH script:
Tagge: And what of the Rebellion? If the Rebels have obtained a complete technical readout of this station, it is possible, however unlikely, that they might find a weakness and exploit it.
The map to Luke Skywalker is obtained through unknown means.
From the novelization:
“Legend says this map is unobtainable,” Poe noted. “How’d you do it?” The older man just smiled, clearly not willing to give up all his secrets just yet.
General Hux isn't even sure that the map exists, implying that it was not stolen from the First Order originally, and that they've never possessed a copy of the portion that BB8 is carrying.
Ren interrupted the general’s impassioned defense. “Keeping the map out of the hands of the Resistance shouldn’t be a problem, then. Yes?”
“Again, this map. Which for all I know may or may not even exist.”
Ren’s voice darkened to a degree that caused Phasma to take a step backward. “I do not think I care for your implication, General. You would be wise to keep such thoughts to yourself. You would be wise not to think them.”
(note that the conversation above is between Ren, Phasma and General Hux)