Open your messaging app, (you should be looking at all your threads)
Press the menu button, go to settings, scroll down to "Extra Settings" the second one, you should see Custom User-Agent. Choose that one, and scroll all the way to the bottom, and select custom, and in the box (it should already be there for you, but if not) "Andriod-Mms/2.0" should be in where, without quote marks.
Also you should set the correct APN settings for your carrier.
BOTH of those settings fixed my issue, and I did not need to reboot my phone to send an MMS message.
I can now send and receive MMS on CM 7.1 stable.
Edited by MattWhitt, 18 December 2011 - 01:52 AM.