Well, if your alarm clock is a Quartz clock, it will remain relatively accurate as long as the quartz remains unmodified or undamaged. With normal usage, other components of the clock will deteriorate before the accuracy of the timepiece is at risk of serious misalignment (I’ll define serious as being an error of 60 seconds).
When will the length of the day be 26 hours? Well, I first ask you to define what “day” means, as it is not a proper SI unit. The second, however, is an SI unit, and one “day” as you use it here is equal to 86,400 seconds. The primary cause of our length of day is the rotation of Earth around its axis (extending to the Earth rotating around the Sun, of course), so to change the number of seconds this takes to do, we would need to change the circumstances which influence the rotation of the Earth. I propose that such changes are impossible for humans to inflict at our current technological level without causing serious repercussions which may end all of humanity’s life. As such, I conclude that the length of day will never be 26 hours on Earth.