That’s about the time that Yahoo (YHOO) expects some of its Mail customers to be without access to the service after a hardware problem in one of the company’s data centers flared this week. In a note published this afternoon, Yahoo communications chief Jeff Bonforte explained that the problem first appeared on Monday at 10:27 p.m. PT and has, at the time of this writing, yet to be resolved.

“The issue has been harder to fix than we originally expected,” he wrote. “We have dozens of people working around the clock to bring it to a resolution.” Chief executive Marissa Mayer quickly republished the note on her personal Twitter and Tumblr pages.

Short of a major data breach, an Internet company’s greatest fear is that its product will go down. Offline, the company cannot gain new customers or monetize existing ones. Its public image is temporarily dented; its profits, permanently. (Yahoo does not break out revenue figures for its Mail product, though it reported more than $900 million in display and search advertising revenues for its most recent quarter.)

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The Silicon Valley company did not divulge how many users were experiencing the outage. But with more than 275 million users in the database, a disruption for just 0.1% of them still impacts 275,000 people, more than the population of Orlando, Fla.. (Imagine unexpectedly closing down Walt Disney World for two days, and see how well that goes over.)

An outage measured in seconds is undetectable to most. Measured in minutes, it is annoying. In hours, it becomes frustrating. In days — as Yahoo Mail is now experiencing — simply embarrassing. On top of that, Mail is among the products that Mayer ordered to be revamped in October as part of her company turnaround effort; though the outage has nothing to do with that effort, it works to erode any goodwill produced by it.

There is a phrase in information technology called “five nines,” referring to 99.999% uptime, or about 5.26 minutes of downtime per year. Some have called it the “holy grail” of service availability; others have have called it only a myth. (It is not.) The term’s prominent usage by service providers in recent years underscores a perceived need for extreme availability in a cloud-based world. So does the rash of news headlines whenever Google’s Gmail (GOOG), Twitter (TWTR), Microsoft’s Outlook.com (MSFT) or any similar service goes down. In an increasingly connected world, we recoil ever more strongly from disconnection.

No one in the business of keeping online services online wants to acknowledge that there is a degree of acceptable downtime, just as retailers would never admit that a minimal amount of unhappy customers is to be expected. Yet as technology industry consultant Phil Simon pointed out in April, when services like these stop working, “it only underscores the fact that they are working the vast majority of the time.”