In almost every case where SMS messages are received and MMS messages aren't there's something glitchy with one or both data connections.
Let's get a little granular with the trouble shooting.
Can you receive MMS messages from anybody else or is it just "her" phone? (Mother? Sister? Girlfriend? Wife? Daughter? Third Dallas Cowboy Cheerleader on the left?)
Are you able to send MMS messages to this person ... and/or anyone else?
Does the sender have any MMS problems with anyone else, or is it just you?
Try turning off mobile data and using wifi only ... and then try turning off wifi and using mobile data only. Do it once for your phone and once for hers. Not the results. Do any messages go through or do they all still fail?
Try sending from different locations to assure you're not using the same cell towers.
I have a buddy who tries to send me MMS messages from one particular location which always fail if i am at work. If I am anywhere else, they go through, and if he is anywhere else they go through. It's just this one location to location problem. Now, at work my cell signal is awful and I frequently lose connection altogether, so I'm sure that has something to do with it, but still it's very difficult to pinpoint the exact cause.