I was getting sms messages that displayed on my Sony Xperia phone as “Message not downloaded” without any more information. I’m using T-mobile pay per month on a factory unlocked Xperia that is new. Turns out the issue is that some text messages that contain data (like a photo or video, or even an icon) are treated as MMS messages. You need to have data enabled and the correct APN (access provider network) settings configured. You’ll need to enable data network first on your Android and either use the settings in the phone for the APN or search for your providers settings on the internet. Problem solved.