Hi Mikael,
I use a slower internet connection at home, a dialup 115 kpbs only, when I tried to fly from LSZH I did encounter a similar issue like yours. Whats your operating system, mine is Windows XP, I just left the system on its own, and after some time popped an error saying, it was unable to communicate to the server. On trying again, it connected and though I got a not-responding window on Pro-pilot on leaving it idle for a while, it connected and I could start flying.
If the problem is persisting, try a reinstall and update the software first, and ofcourse you should send a mail as mentioned above by Bruno, as it could help sort problems out of Pro-pilot as any.