There are a couple of possibilities. The most likely cause is that the person sending the text isn't actually sending a picture. (They think they are, but it's not really being sent.) Sending a picture by text is actually sending you a link to a picture stored on an MMS server. If the sender's APN information (which includes that server's address) is set wrong, they're sending you what's basically a "link to nowhere".
Or the process could be getting corrupted in a few different other ways.
The only way to tell for sure is to deconstruct the message (that takes some specialized software), finding the link and looking at it. There may be no such file on the server, there may be no such server, etc.
Check for commonality in the problem. Is it always the same person whose pictures don't get through? Is it always people using iPhones that are causing the trouble? If you can narrow it down, some people can suggest some things you can try to at least figure out what the problem is, if not also how to fix it.
(Create a free account here, so you can post answers to this thread, instead of starting a new one every time you post. That way a short answer has the question in the thread, and people will know what you're talking about.)