This is a problem with Bitcoin-Qt/bitcoind/Bitcoin Core (whatever the heck it is called these days). Armory is stuck until that is resolved.
I suspect this can be resolved by manually starting Bitcoin Core and reindexing the blockchain. That should rebuild the databases that Bitcoin Core uses. As much as we hate redownloading the blockchain, that may be required if you get the exact same error after you reindex. Or if you don't know how to reindex, just redownload. Armory includes a new BitTorrent downloader on Windows and Linux that downloads the blockchain as fast as your bandwidth will allow (sorry Mac, you get decent compatibility in 0.91, but not any of the torrent features). It still takes a while for Bitcoin Core to verify it, but the whole process is like 5-10 hours, instead of 24+
We have a new feature in 0.91-beta: "Help"->"Factory Reset". It will wipe all settings, unconfirmed tx, and all databases for both Bitcoin Core and Armory. I meant to have an option that allows you to wipe the databases without deleting your settings, but not much I can do about that right now. Your wallets will still be untouched, and automatically loaded when you restart.
If you go that route, make sure your wallets are backed up (as an extra precaution), use the factory reset and wait.
I'm now reindexing and if doesn't work I'll install Armory 0.91