An unofficial fix has been discovered and requires some minor tinkering. It'll likely void your warranty, but if you have a sense of adventure and a dead Zune, the fix is reported to work without issue.
Then just an hour ago or so, we learned that a software glitch came into effect with the leap year clock. Microsoft's response then:
Q: What is Zune doing to fix this issue?
The issue should resolve itself.
Indeed. By midnight your Zune should be back to normal, at least until the next leap year in 2012 or when Microsoft issues a patch fixing the bug.