I had a problem recently where the iFly would download 1 or 2 files (out of many), but no others. During most of its attempts a red box would pop up saying that the file download failed, yet it would keep trying from where ever it was (but would never successfully complete).
I know it was properly connecting because it would find the server, authenticate, download the file manifest, etc. One other weird thing that I noticed was that after a file download failure, the transfer rate would be reported as a negative number.
I managed to fix this problem with a single tap: I changed from WPA2 to WPA on the WiFi setup page for this network. I don't know why this worked, but I swear it is the ONLY thing that I changed.