There may be some dragons hidden deep below the surface where vulnerabilities can hide, as is the case with anything, but when it comes to this question, it comes down to how you've deployed your app, I think you've got a far bigger attack footprint when it comes to your own code than being vulnerable via Durandal or Require.
Firstly, the most common approach for deployment of Durandal apps is to get rid of Require entirely anyway, by using something like Almond as part of your build and deploy. This action takes Require out of the loop, and Almond (AFAIK) only supports "requiring" local resources and cannot reach out over the network anyway. Hence when you use something like Gulp/Grunt/Weyland to mush everything together into one script, you can be 100% sure that the only objects Durandal will ever get hold of in your app are the local ones compiled into your script. Unless an attacker can actually modify your main script (on the server), they don't stand a chance of exploiting framework code in the way you are asking about - and if they're on your server, you've got bigger problems :)
Now of course you can break out of this paradigm and go ahead and deploy the entire thing with Require fully enabled, which again opens the door for your question, so it still has merit. The way Druandal loads (discovers) views and viewmodels as far as I can tell is by various opinionated pattern matching strings/objects and the code it uses to do this can be overridden by your own code to bring your own view loading strategies for example. The default ones that come with Durandal are pretty benign and don't seem exploitable to me on the surface, but I suppose anything is possible given enough brainpower.
What's way more likely though, is that you allow some data entry in your own code to go unescaped/unsanitized which comes back to the browser generating a XXS attack. The potential attacker could spend ages looking for a vulnerability in compressed/uglified framework code, be it Require or Durandal, and of course they could easily exploit their own session by Requiring a malicious script forced through Chrome dev tools or something to test a POC on your code, but that same attacker getting another user on your site to Require that same malicious script without having access to their session would be incredibly difficult if not impossible. They first have to get in on the victim user session, things that open the door to that kind of the thing are your code, especially how you sanitize your data capture etc. The low hanging fruit so to speak. I can't see them getting value wading through reams of uglified framework code unless there was a big reward in it for them and a chance of success.
Maybe Rob would have a better idea and shed more light, but for me this is how I see the current landscape of attack vectors.
So the question is - how are you deploying your stuff? All squished up in a single script, or with full Require calling all the pieces to the party over http requests? While the first is likely safer due to less variables in the mix, I still feel the second is much less prone to attack than your own actual code and functionality on the site itself - especially if you take user input in any form. I would focus on locking that down first.
Hope that helps,
Cheers,
Rob G