The ability to function offline (using maps already downloaded to one's phone) is arguably one of HERE's greatest strengths, Rachael Alice. Indeed, the main reason why I keep it on my phone is as a backup, in case I find myself without a cell signal and thus unable to rely on Google Maps for navigation. (Admittedly, GMaps can function offline, but it's sort of a kludge that way, its ability to download and use maps being somewhat limited.)
I have no idea why it can't find a route between Italian cities. Maybe you only think you downloaded all the necessary maps, Pinco Pallino. If you're absolutely sure you've downloaded all the necessary maps, maybe turning off your phone and restarting it would get HERE working properly. Maybe your copy of the HERE software is corrupted in some exceedingly subtle way, which prevents it from providing you with the necessary routes, so an uninstall and reinstall would be advisable. Maybe there's a problem with your phone's hardware or firmware. Maybe something else entirely - like some odd choice of user settings or something.
If you figure out what's wrong, I'd appreciate hearing what it was.