After several hours of researching possible workaround for this bug I found this curious solution:
If you experience problem with disappearing covers install this free app "Battery Doctor":
https://itunes.apple.com/nz/app/batt...446751279?mt=8
and run:
1) Memory -> Boost
2) Junk -> Clean up cache.
You should regain some disk storage and covers thumbnails in Kindle for iOS 5.0 should be visible again.