I had the same issue and I found a way around it! :)
I just made a reddit post about it: www.reddit.com/r/jailbreak/comments/29k69o/fix_for_pangu_11_stuck_at_jailbreak_timeout/
Here's the text I wrote over there:
I just tried to jailbreak my iPhone 4S on iOS 7.1.2 with Pangu 1.1 and a few minutes after you have to open their Pangu app on the phone, when it's done injecting stuff, the phone reboots. Pangu then says to wait and not to disconnect the phone, then a bit later it says to unlock the phone for the jailbreak to continue. BUT I have many, many apps on my phone (64GB phone with about 600 apps) and therefore it takes quite a while to reboot. Pangu seems to be a bit impatient and for me, it always displayed "Jailbreak timeout" about 20 seconds before the phone was even finished rebooting. After that, there was no way to just "resume" the jailbreak, I always had to restart the whole process and it always failed because of the long reboot time.
First, make sure that you have disabled the passcode lock on the phone and also make sure that iTunes isn't opened automatically when the phone is connected or at least immediately close iTunes after it opens by itself. That alone might already help you get around the timeout issue. But I had already taken care of those things beforehand and still got the timeout.
So, as soon as it says "Rebooting phone, do not disconnect" and as soon as the Apple logo is displayed on the phone, I disconnected the phone. Because in that short time when the phone is OFF, it doesn't make a difference to the computer whether it is connected or not - as far as the computer is concerned, there's no phone to detect. And as far as Pangu is concerned, the timeout timer doesn't seem to start until it detects that a certain phase of the reboot is done. And luckily, it seems that Pangu also doesn't need to inject anything else during the reboot, so just let the phone boot by itself while it's disconnected - it can take as long as it wants now. When it's finally done booting, maybe also unlock it first, so that you're on the home screen. Then just reconnect it to the computer and Pangu will finish and finally install Cydia! :)
TL;DR: Despite what Pangu tells you, just disconnect the phone while rebooting (just as the Apple logo appears on screen) and connect it again when it's all done booting - that should get around the timeout issue.