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A computer glitch or hardware breakdown by itself would just be Chairs. Really need some additional context to make any suggestions- what sort of problem and decision are we talking about here?
Is The Alleged Computer finally breaking down entirely, but Alice is too attached to replace it? Is the computer running an artificial intelligence that will effectively die if shut down? Is the automated shield system on the spaceship breaking down during a critical situation leaving Bob to manually chose which parts of the ship to protect from the Asteroid Thicket?

Something goes wrong with a computer making the protagonist making protagonist have to make a hard decision