I'm not sure how to exactly reproduce this bug, but I do believe it's always solved by shutting down HEM2 and all Full Tilt windows, followed by starting HEM2 first, and only then starting Full Tilt.
Whenever this happens, manual imports always work, of course, but that doesn't kickstart the auto-importer; you have to manually import every few minutes for that to be very useful with the HUD.
Stopping the HUD and auto-import and re-starting them also does nothing.
So since this is only noticed once it has happened, the only real solution I know is to leave all tables (with downsides such as having to re-start with 100 bb in case you've gained, or leave good tables for non-rush players) and restart.
I did notice one interesting thing, not sure if it can matter: the hand history file has properties
FT20140125 Bazinga (6 max) - NL Hold'em - $0.02-$0.05 - Entry 1.txt
Created: 25 Jan 2014, 11:52:33
Modified: 25 Jan 2014, 11:52:33
Accessed: 25 Jan 2014, 11:52:33
... even though the current time is 26 Jan 14:28, and the hand history is continually updated as I keep playing.
This is with HEM2 22.214.171.12490, trial version.
Edit: It may well also be relevant that this is in a VM (VMware Fusion), running Windows 7. I put the host computer to sleep during the nights, but the VM is always running, and HEM2/Full Tilt are also often "running" overnight.