You haven't said how you are streaming the video.
Are you streaming using an app (GoFlex Access aka hipserv), opening the file on a network connection, using seagate share in a web browser or over UPnP? Are you using the same method when connected with 3G and when logged on to your own wifi? (I guess that would rule out UPnP)
The GoFlex Access app on my phone often gives the unsupported format message because the app has it's own player that doesn't seem to play very much.
The annoying part is that it doesn't give you the option of downloading the file. For example I have .ogg audio files that I can't play in the hipserv app but since the app doesn't recognise .flac files as media files it doesn't try to play them so they download and I can play them on my phone's own media player.
Goflex Access behaves the same for me whether I am connected over 3G or on my home wifi.
But If I open the files over the network then they play in the device's inbuilt media player with no problems.
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For the sake of your own health and sanity, if your data is important to you, keep a second copy on another storage (a backup)
