This is a recent issue - maybe started two, three weeks ago. My phone is a One, updated to 4.4.2
Whenever I receive group text messages sent by someone I've already received texts from, the text shows up as "downloading". These are just text messages, no videos/pictures/HTML links. The download fails 9/10 times and I have to either wait a couple hours ( ! ) or constantly hit "retry download" for it to show up. I haven't noticed this problem with messages from numbers not saved to my contacts - in fact, there was a period of time where friends of the person who last owned my phone were sending group messages and I got every single one of those immediately, including pictures/videos.
These group texts are for work, so while I haven't had a download completely fail and I can't read the message, I don't want to risk that happening.