I've been having this issue with my phone not sending or downloading picture messages. Well, I am using Wind Mobile for demo, but it should work for others (prove me correct, by clicking the "thanks" button):
1. Add internet.windmobile.ca as APN #1
2 APN #2:
Name: Wind CA MMS
MMS Proxy: 184.108.40.206
MMS Port: 8080
Type: LEAVE THIS BLANK!
The problem with mine was the type was set to mms.
When you're done, make sure that this APN (because my phone only lets me select 1 APN, so select internet when you need internet, and mms when you need mms) is selected when you need to download/send MMS (and maybe a quick airplane mode network refresh). This ain't the prettiest way, but it gets the job done!
Hope this help.
[Props to polkiu over at howardforums for this]