Ellen Ripley seems to complete the deactivation of the request either physically or via a voice command, and Mother rejected accomplishing the task. She didn't want to or wasn't able to?
TL&DR version: Ripley missed the window to disarm it by seconds.
If you look at the system when she's arming it, it makes it clear that there's a 5 minute window to deactivate
When she approaches the 5 minute cutoff, you can hear Mother counting down; As Todd-Wilcox mentions in the comments, you see her pushing down on the columns to try to make it go faster, since she can see that she's right at the edge of the time... and she doesn't make it.
She finishes what she's doing at one console, and runs over to push the levers back up to finish the abort... and you hear mother say that "The Option to Override detonation procedure has now Expired." Ripley was still pushing the levers up when mother starts making the statement, which occurs right at the 5 minute mark. (First, you see it hit 5 minutes, then it switches back to Ripley pushing the lever up.) (One is still all the way down, and she's partway pushed the other up, when 5 minutes hits and Mother makes the announcement.)
She finishes the override steps as Mother hits the word "Now" in "The Option to Override detonation procedure has now Expired."
If it's still up, you can watch the whole deactivation process here, where I got the screencaps. She misses it by seconds, but she does miss it.
Why should mother not help anyway? It's been a while since I've seen the movie, and it might be mentioned somewhere else, but I assumed that since her next comment was "Mother? I've turned the cooling unit back on. Mother?!", that the self-destruct was basically allowing the ship reactor to meltdown (although, for some reason the ship would detonate), and 5 minutes was the point-of-no-return; Mother wasn't trying to be unhelpful, it just wasn't possible to abort, at that point.
Why should mother not help anyway?
The out-of-universe explanation is a countdown adds tension, and they needed to show Ripley being unable to turn off self-destruct. They don't need to explain why, explaining why would be distracting, it's enough that she tries but she can't.
K-H-W's answer is good, there is a physical point where self-destruct cannot be stopped. While it may be true that there is such a point, having it a exactly 5 minutes is a bit too neat. This isn't Star Trek where they can calculate everything down to the last second. The Alien universe is gritty and messy. Even if 5 minutes was determined at the factory, with the state of repair of Nostromo it's hard to believe anything works to factory spec.
An alternative, or additional, explanation is that the 5 minute mark is a security mechanism: Mother is programmed to not allow any override.
Why would Nostromo, a civilian cargo vessel, have a self-destruct mechanism in the first place? Because there are situations when leaving the ship intact are far, far worse. For example, if your ship is out of control, drifting towards an inhabited planet, and carrying disease or very dangerous cargo, you really want to make sure its reactor blows up before it gets too close; you don't want any panicking crew to stop the process. Or maybe your ship is being boarded; you don't want any plucky heroes turning self-destruct off with 1 second remaining after you've left.
The Emergency Destruct System describes it as a "Failsafe Warning" and cancelling the self-destruct as a "Cut-off system" implying self-destruct is an active process which can be stopped.
If you set self-destruct and let it tick down to T-5 minutes, the people who programmed Mother assumed that everyone is leaving or has already left and that you absolutely do indeed want to blow up the ship wholeheartedly. They didn't contemplate you'd be blocked from the escape pods by "something never recorded once on over three hundred surveyed worlds".
When Ripley tells Mother she's turned the cooling units back on, she doesn't expect Mother to do anything. Mother doesn't have voice commands, you need to go into a special room full of blinking lights and type on a keyboard. Mother can't hear her, and Ripley knows that. She's just doing what we all do; she's yelling at a computer in frustration.
In the original screenplay, the self-destruct doesn't appear to be an intentional self-destruct system, it was just Ripley using her knowledge of the ship's engine to cause the power core to explode.
MOTHER'S VOICE: (o.s.) Attention. The cooling units for the light-plus engines are not functioning. Engines will over-load in four minutes, fifty seconds...
When she tried to remediate her actions less than two minutes later, the damage she'd already caused was sufficient to result in the ship becoming a ticking timebomb. Again, note the absence of a strict cut-off time limit.
MOTHER'S VOICE: (o.s.) Attention. Engines will overload in three minutes, twenty seconds.
INT. ENGINE ROOM - CUBICLE The door crashes open, Ripley comes pounding in.
The chamber filled with smoke.
Engines whining dangerously.
Ripley breaks out in perspiration from the intense heat.
She runs to the controls.
Begins throwing the cooling unit switches back into place.
The sirens continue sounding.
MOTHER'S VOICE (o.s.) Attention. Engines will overload in three minutes.
Ripley pushes a button and speaks into it.
RIPLEY: Mother, I've turned all the cooling units back on.
MOTHER'S VOICE: (o.s.) Too late for remedial action. The core has begun to melt. Engines will overload in two minutes, thirty-five seconds.
The official novelisation also strongly agrees. Mother advises her that the process is simply too far gone to rectify.
Gasping for breath, she leaned against the hot wall as she jabbed a button. 'Mother, I've turned all the cooling units back on full!'
'Too late for remedial action. The drive core has begun to melt. Reaction irreversible at this point. Implosion incipient, followed by uncontainable overload and subsequent detonation. Engines will overload in two minutes, fifty-five seconds.'
It would appear that the film's makers realised that audiences need a more explicit explanation of why the ship is going to blow up and put in place a handy-dandy self-destruct sign to explain what's happening. Having done so, they also then put nice round numbers in place to make it easier for audiences to realise why it wasn't fixable after she'd changed her mind.