Multimedia Messaging Service has limitations. With videos and HD photos it just won't send. I have run into this with videos on two of my phones. I then attach them to my GMail account and send as email. If you change the resolution in the video settings to the lowest setting and keep the video under 30 seconds I have been able to attach and send without any difficulty.
You cannot have the video resolution at the maximum settings it is too much data for a simple mms. Either use the lowest settings or use email or upload to Drop Box and send a link to the file.
some phones even have a specific setting for recording videos for "mms." you can't convert them though. you have to shoot them in mms mode, and it's very poor quality.