Juniper Network Connect hangs at “Establishing Secure Session” after upgrading to OS X El Capitan
As of July, it appears Juniper is still working on this. The conclusion of that thread claims you can get Pulse working again by:


Downloading the Symantic Certificate Authority
Rename Symc_Cross_Root.txt to Symc_Cross_Root.crt
Open Keychain Access, select 'System' in the left pane
Choose File>Import File... And navigate to the file you just renamed
If you see something about a VeriSign class 3 certificate you're doing the right thing. Click the drop down next to 'Trust'
Select 'Always Trust'. If you get a little blue icon next to the cert, you should be good to go. 


Please note I've not tried this myself. It's a hack to get around unpatched and misbehaving software. While I generally like Juniper, I don't use their software products and I don't trust their tech team as far as I can throw the SRX550 that once shit out on me during a server move. This advice is coming to you from a stranger on the Internet, your mileage may vary, failure to fully test before upgrading in a production environment may cause herpes, etc. etc.