If you're live streaming I would not expect the Movie Fragment Random Access (mfra) box to be present. I believe it is used only used server side to allow for easy fragment extraction and is never passed across to the player. You'll also see the mfra in any mp4 files you have on your local disk.
What you are likely capturing is the individual fragments of the stream. These are made from the Movie Fragment (moof) and Media data (mdat). The moof has two other atoms inside, Movie Fragment Header (mfhd) and the Track Fragment (traf).
If you are trying to reassemble the file from fragments you will need to do this (conceptually)
[ftyp][moov][fragment][fragment]...[fragment][mfra]
Where each [] is a box that may contain other boxes. See Alex Zambelli's blog for some good info. You will need to create the [ftyp][moov]
and the [mfra]
to properly represent all of your other fragments.