I have the same problem. I'm currently on both network and wifi. It happens in both cases. No mms or group messaging will work. iMessage is fine with pictures and groups. I've got MMS and group messaging turned on. I'm not resetting my phone completely. Please tell me there's another fix.
I depend on my messaging service to work right. Lets get this figured out. Is this happening wit ha specific contact/group? Anything change on the phone when this issue began? What model iPhone do you have? AlbertoR_VZW