Does it shut down completely, or just lose the connection and go to non-charging mode?
I'd probably try a new cable first- they're cheap, and that's likely what it is. If that doesn't work, I'd be tempted to do a factory reset on your kindle (if you've got all of your books in calibre, it's easy to re-populate it). Is your calibre updated to the latest version?
If a new cable doesn't cut it, and the newest version of calibre doesn't make a difference, I'd call Amazon customer service. At the least (even if your warranty has expired) they'll probably give you some credit towards a newer Kindle.
I'd probably try a new cable first- they're cheap, and that's likely what it is. If that doesn't work, I'd be tempted to do a factory reset on your kindle (if you've got all of your books in calibre, it's easy to re-populate it). Is your calibre updated to the latest version?
If a new cable doesn't cut it, and the newest version of calibre doesn't make a difference, I'd call Amazon customer service. At the least (even if your warranty has expired) they'll probably give you some credit towards a newer Kindle.