I noticed a similar issue on my iPhone 4, with iOS 5.0.1. I found that if I went to the full site, rather than the mobile site, I was able to download the GPX file into Geosphere. It looks to me like the mobile site has some features that don't play well with the Geosphere browser. The full site wanted me to install flash but that wasn't necessary, or even possible. I have the Box.net app installed but there doesn't appear to be a way to get Geosphere to work with it. Sounds like we need to prod the Geosphere folks to update their app.
Worked fine until I last tried to import the info. into Geosphere last week. Give me more info. on how you DL'ed the PTX file into the Geosphere browser. I can get to the full site with box.net, but the Geosphere is only an app. on my iTouch. Not sure how to access the full site except through the iTouch -- or maybe I'm misunderstanding your post.
Thanks to everyone who is trying to help figure this out. I'm pretty frustrated right now.