The general consensus in the forums is that the power units in the Time Capsules seem to be failing. Apple has not, to this point, officially recognized this issue, though users with the problem can experience some relief if they have AppleCare on one of their Macs at home. AppleCare covers peripheral devices made by Apple, such as the Time Capsule, AirPort Extreme Base Station, AirPort Express, Apple Keyboards, and the Mighty Mouse.
For users that do not have AppleCare, the situation gets more frustrating. Your option is to pay for a service replacement on the device--in which case Apple will take your old Time Capsule, including its hard drive and all the data (which they will destroy). Your other option is to keep your old Time Capsule and attempt to fix the hardware yourself. It appears that the capacitors are the main culprit of the failures--a part which many electronics repair shops should be able to fix.
We will certainly keep an eye on this story and let you know if/when Apple makes an official comment regarding the Time Capsule failures. Experiencing issues, have questions, want to let us know about an issue we should report on? Email Us!