Apple has conceded a fault with select models of their Time Capsule wireless backup drives, whereby the low-profile NAS powers down and then refuses to restart. According to a new Knowledge Base article, Apple will repair or replace those units, including transferring data from the old Time Capsule to any new model supplied.
Models covered by the new repair/replacement agreement will have been sold between February and June 2008, and has to have a serial number that falls in the region between XX807XXXXXX and XX814XXXXXX. Assuming that fits, the next step is to get in touch with Apple Care or make an appointment with your nearest Genius Bar; Apple will either fix it in-person at their stores or via mail.
If you've already paid to have your Time Capsule fixed then Apple's advice is to contact the customer care team to arrange a refund.