We have SharePoint exposed externally via ForeFront TMG. The SSL connection terminates at TMG and is then proxyed internally over HTTP. Our "hosted" application is accessed internally by http://hosted.corp.com and the same app externally is accessed by https://hosted.corp.com. Internally all results show up fine, but externally we get no results. Our other web applications which are crawled by the same service work fine internally and externally.