The scenario is this:

iPads (iOS 5) running Share Plus Pro
SharePoint 2010 server
Microsoft Forefront publishing the SharePoint site

The Forefront rule for the SharePoint site is configured to allow the client to authenticate directly ('No delegation, but client may authenticate directly'), and the Listener is configured to use 'HTML Form Authentication'.

I can access the SharePoint site using Safari.  It takes me to a Forefront authentication page:

and when I have authenticated it lets me in to the SharePoint site.  Success.

If I configure SharePlus Pro to use Windows Authentication or Forms Based authentication I get a popup 'Authentication Required' prompt. I enter my credentials, click Continue, wait a second or two and the popup reappears.  And so on ad infintum.

If I configure SharePlus Pro to use Web Login or Office 365 authentication I get the Forefront screen as shown above. I enter my credentials and get an Authentication Error 'The operation couldn't be completed. (NSURLErrorDomain error -999.)'

I've spent a couple of days unsuccessfully trying to get the right combinations of SharePoint, TMG and SharePlus.

If someone could point me in the right direction it would be greatly appreciated!