I have this problem, too.
It stops downloading after a short time.
I have the same LiberKey version 5.0.1217 and I use Windows 7 64bit.
My antivirus is PC Tools Internet Security. Deactivating it does not help.
The speed of the internet connection might be a problem. I have only about 200kb/s.
Here you can see the use of my internet connection when I want to Update my LiberKey.
After starting the download the progress bar moves a little bit. But then it stops and nothing happens anymore. I already tried to wait about an hour but nothing happened.
My LiberKey:
LiberKey 5.0 - 20101217175330 - de (0.30)
Root folder: H:\LiberKey\
7-Zip - 9.20 - Installer\7z.exe
LiberKey Inst - 1.2.0.99 - Installer\LkInst.exe
KEY Files Assoc' - 1.8.0.30 - KeyFileAssoc\KeyFileAssoc.exe
LiberKey Menu - 5.0.0.194 - LiberKeyMenu\LiberKeyMenu.exe
LiberKey Portabilizer - 2.0.0.371 - LiberKeyPortabilizer\LiberKeyPortabilizer.exe
LiberKey Apps Closer - 1.0.0.32 - LKAppsClose\LKAppsClose.exe
Liberkey Apps Version Checker - 1.3.0.179 - LKAppsVCheck\LKAppsVCheck.exe
LiberKey Disk Ejector - 0.1.15 - LkDiskEjector\LkDiskEjector.exe
LiberKey USB Eject - 2.0.10 - LkDiskEjector\LkEject.exe
LiberKey Portable Desktop Shortcuts - 0.1.0.54 - PDS\PDS.exe
WAK - 1.0.13 - WAK.exe