So I started to search through the internet and I found something in the forum of Juniper itself:
Snow Leopard Network Connect Fix:

It Seems that Snow Leopard has changed some of the internal structure of Network Connect and removed the frameworks directory as well as messing up the permissions where changed.

After reading the workaround carefully, I searched for a Juniper Network Connect Installer and found one via Google. I installed the application and as expected the vpn tunnel didn’t work yet. As written in the workaround thread I have to do 2 things manually:

• Change the file permissions of the following folder (version number stands for the installed NC version – in my case it is 6.4:
  sudo chmod 755 /usr/local/juniper/nc/[version number]/

• Create the folder ‘Frameworks’ in the Network Connect application folder:
  sudo mkdir '/Applications/Network Connect.app/Contents/Frameworks'

After these two tweaks I started another attempt – and it works!

On several websites I read about connection timeouts and disconnections. A guy wrote that NC isn’t able to clean up the routing table on establishing of a connection. One trick which should work is to disable all unused network interfaces. I can’t commit this problems, and I hope this resists as long as Juniper releases their update.