I would indeed discuss it with her teacher. If the teacher doesn't appear to seem entirely confident in her answer, I would consult with other teachers as well. I would not add more lessons; they are likely to do more harm than good. Also, while she might "grow out of" the problem, she is likely to resolve it more quickly with help and guidance.
That said, there are things that you can do yourself to help. For a start, this doesn't appear to be a physical inability, since she can follow a melody without making mistakes. So, the most important thing is to be patient and positive. Be very careful not to yell at her or give her negative reinforcement. Negative input yields negative output, despite the persistent human belief to the contrary. Have confidence in her ability to fix it, and she will be much more likely to develop the same confidence.
Now, it seems more likely to me that this is a psychological block than some sort of (minor) learning disability. In other words, the reason that she can't sing solo is simply because she is afraid that she can't. If so, you can help her by inventing some exercises and getting her to do them. Don't try and tie these exercises to the problem, present them with a "let's see if you can do this" sort of attitude. Be curious about whether she can do the exercise, not whether she is going to learn to sing a melody without accompaniment. Forget about that, so she can too. Be creative, inventive, and playful, and so will she.
Start with something very simple. Give her a note on the piano, and ask her to sing it. Then, give her a note and ask her to count to three and sing it. Get her to count to five and sing it. Once she can do this (if she has trouble with this, then there may really be some sort of minor learning disability, in which case I would consult a specialist in learning disabilities for further testing and diagnosis), ask her how she was able to do it. She'll probably tell you that she just remembered the note. Tell her that's great, now let's see if you can do the same thing with two notes. Give her two notes. (Start talking with her about intervals at this point if you think it's a good idea.) Once she gets two notes, try three.
If she can wait five seconds and sing back three notes, then you can explain (or perhaps remind her is a better term) that if she can remember three notes she can remember more. Explain also that this is exactly how people sing without accompaniment; they're simply running through songs in their head (as she just did with the melody notes) and singing back what they remember. At some point, you should see the "light dawn" when she suddenly realizes that she can do this and understands how.
Hope this helps!