SharePoint 2010 People Picker Authentication Issue

We are experiencing a problem in our production SharePoint environment with a specific piece of functionality. We have two Web Front Ends load balanced via F5 Big IP Hardware Load Balancers.

The Web application we have uses standard SharePoint People Picker functionality to add users to a defined set of SharePoint groups. When we access the site through the load balanced VIP address we can search for users and the users are returned from AD but as soon as you click the OK button on the Grant Permissions screen a Windows security Login Box is popped up and you cannot go any further.

If you go directly to one of the Web Front Ends and bypass the Load Balancer this works fine as it does in the Development environment whicxh doesn't go through the Load Balancer.

The SharePoint site is set to use NTLM authentication as is the site on IIS. This must be a problem which is a combination of the Load Balancer and Authentication somewhere but I am struggling with this now.

Any help would be appreciated.