A local swf file that loads data from a server fails to load the data in Flash Lite 3.* players.
Solution
Check that the server has the required crossdomain.xml and that you are loading this before making any data requests.
Detailed explanation
If you are accessing anything remote from a local file then you will have to do the following:
Put a crossdomain.xml file on any server you are accessing that allows any domain access. Or have a proxy script on one server and use that as a gateway to anything you want.
Publish your swf as having 'Network Access Only'. So File > Publish Settings > Local Playback security > change 'Access local files only' to 'Network Access Only'. If you don't do this then your swf won't even trigger the network connection dialog on the device, it will just die silently. Its important to note here that the default is local files only so ANY old content that uses a network connection will not work in Flash Lite 3 until you re-publish it with the correct settings. See playback security information.
Once you have everything in place before you make any remote calls you'll need to load the crossdomain policy file.
Be aware that neither Device Central or the Flash IDE currently enforce the new security measures, so you won't realise any issues until you test on the device.