Reasons for MMS to fail while sending?
As I don't use MMS, I had to check first: Looks like MMS have a APN configuration separate from your (normal) internet APN. Here are some useful ressources:


How to set up Internet and MMS APN on Android for any operator A youtube video
How to: O2 UK APN Settings for Android iPhone iPad just as an example showing you need both APNs (Internet + MMS) -- if O2 UK is your provider, all the better :)
Support: APN settings for data and picture messaging (MMS): Android T-Mobile


Quoting from the t-mobile link:


  When you receive errors trying to send picture messages (MMS) or access data or the internet, confirm your Android phone is set up correctly. This is usually a problem with device settings.


Which seems to confirm my initial suspicion :)

So if you let us know your provider, plus your current APN configuration, maybe we can give more detailled help. On the other hand, the easiest was would be asking your carrier for the correct APN data directly (or visit his website, where they are probably held available -- as my examples from O2 and t-mobile show). A Google-Search (for " mms apn") could also prove useful.