GILORA: Starfleet code requires a second backup?
O'BRIEN: In case the first backup fails.
GILORA: What are the chances that both a primary system and its backup would fail at the same time?
O'BRIEN: It's very unlikely, but in a crunch I wouldn't like to be caught without a second backup.
Makes perfect sense for O'Brien, DS9 had serious backup issues in the first couple of years
The Forsaken (season 1 episode 17)
LOJAL: I've been reading the reports of your Chief of Operations, Doctor. They gave me the impression that he was a competent engineer.
BASHIR: Chief O'Brien? One of the best in Starfleet.
LOJAL: Then why aren't the backup systems functioning?
BASHIR: Well, you know, out here on the edge of the frontier, it's one adventure after another. Why don't I escort you back to your quarters where I'm sure we can all wait this out.
Rivals (season 2 episode 11)
KIRA: My terminal just self-destructed.
DAX: What?
KIRA: I lost an evaluation report I've been working on for weeks.
DAX: Even the backups?
KIRA: Even the backups.
There's a reason to have a backup to the backup by Destiny (season 3 episode 15)
https://www.youtube.com/watch?v=UaPkSU8DNfY