Time Capsules owners in considerable numbers are filling Apple's discussion forums with complaints about the product, in several different topics (see an example here). Users say the devices are simply stopping working from scratch as they approach (or slightly exceed) 18 months of use.
Apparently, the problem is affecting owners of the first Time Capsules sold by Apple, which started shipping in early 2008. Hardmac suggests that the cause of the defects lies in a flawed component of the power source, which cannot be replaced by anyone without loss of warranty, and even if it could, the period covered by Apple would have been long gone.
The first recommendation for anyone who is passing through or has already gone through this is to send complaints about the problem to Apple, and see if it can recognize the existence of any manufacturing defect in the affected Time Capsules. In addition, you can take advantage of AppleCare's extended warranty to exchange your product outside its nominal warranty period.