This usually works for me.

1. In Armory:   Help -> Rebuild and Rescan databases

2. Close Armory.

3. Open Windows Task Manager, make sure any Armory process is not lingering.  (ArmoryDB.exe tends to stay stuck)  Kill those.

4. Re-open Armory.  Wait for it to complete scan and rebuild.

If you still end up in an Offline state, repeat step 2 to 4 (close armory, kill ArmoryDB, re-open armory).   I usually get armory back online after 1-2 tries. 

You can also try to open bitcoin core directly when armory is closed (between step 3 & 4), wait for it to sync and close it properly.


That said, it should not happen if you closed Armory correctly.  I end up in this state only if windows crashed or decided to reboot for an update without prior notice...