SharePoint "Open with explorer" publication with TMG

Hi,

I'm having troubles for SharePoint "Open with explorer" feature. It work's perfectly inside my LAN (After a few configuration on IE and on the reg of my Windows 7 computer). Then, I published my SharePoint site with TMG 2010 with SP1: Everything works except one thing, I'm prompted (But only the first time) when i'm using the "Open with explorer" feature. My client doesn't want to be prompted when he use this feature.

I checked the credential manager, 

I checked the reg

I checked the security settings and connection settings of IE 9 x86

I tried to switch to basic authentication for my SharePoint Site and TMG.

All my modifications did not change anything on the situation... I'm asking social technet because i'm running out of ideas :( ...

Charles Borcke MCTS SharePoint for Exakis