JamieBennet... Since there appears to be a consistency of the issue with applications that have any kind of input monitoring or input control between hardware and OS (in other words, anything that deals with mouse input, keyboard input, or anything similar), it's possible that Junos Pulse has a security feature built into it that protects against automated keyboard entry for its VPN logins. If it's using an Apple API call that does that, it might be triggering OS X's security block, just like the other apps like MagicPrefs. I use Junos Pulse myself for our company VPN, but I specifically have Junos added to my permitted accessibility apps, so I have no issues. You might wish to try going to System Prefs > Security & Privacy > Privacy > Accessibility, and then adding the Pulse software to the list of apps that can control your computer.
Also, something else that I do with Pulse, is that I only ever run the app when I'm connecting, and exit when I'm disconnecting, rather than leaving the app in the notification area all the time. Pressing Command+Space and typing "pulse" and hitting enter is not much slower for me than clicking it in the menu bar. Of course, if you're a remote worker and must have Pulse running all day, that could get annoying. Also, are you using the latest version of Pulse? There was a pretty significant update a couple of months ago. Maybe that will help. Anyway, hopefully the above tip will work for you.