I suspect quite a few teachers suffer from 'performance' nerves, including myself, especially in front of our students who respect us and expect a lot from us. The most important thing for me is to be able to deal with it.
I think some good points have been made my Aquarelle and diapason, but I do also think that it is beneficial to have a piece or 2 up your sleeve to demonstrate
your playing ability, should a student or student's parent ask to hear you play. I know it is hard - I face this every lesson with my more advanced students who ask me to play things for them, but I always make sure I have a couple of contrasting pieces of my own prepared and ready to bring out. (it helps that I am also a pianist, as well as a teacher, so I have pieces prepared for recitals and festivals most of the time that I can draw on).
My sight-reading is good and I play to a high standard, but just as with stage performance nerves, lesson performance nerves hit me inexplicably and when I first started teaching, I made a couple of mistakes in a very basic piece that I demonstrated to a pupil. That really threw me, and I decided to always be prepared for lessons, however basic the pieces are. So I now make sure that for my students of grade 2 level and above, I always play through their pieces a couple of times a week. I know they are simple, and they don't need any work at all, except that I am comfortable with them, which eases the situation in the lesson.
If a student presents me with a new piece, asking me what it sounds like, I usually say that we should stay on track this lesson (they usually present it when we're about to do something they're not keen on anyway!) and I will show it to them next lesosn, when I have had a chance to look at it, as I am not familiar with the piece. I don't feel that this is copping out and it gives me a chance to run through it in the safety of my home before presentin it to them. If however I find myself in a situation where I have to play that new piece right then and there for whatever reason, I think sometimes you have to 'suck it up' and just do it.

I have found that a lot of the time it is OK if you consciously tell yourself that you are doing it for the benefit of the student. I just take a deep breath to calm myself and play it. I might end up having to stop half way through if nerves are really kicking in, but I just say that I don't want to play the whole thing, because I want them to work on it themselves. (I have a lot of very musical students who if I play them a piece, they will not read the music ever and just work it out from what I've played).
Although this is how I deal with things, I do think that ultimately, I/one has to work on the nervousness problem and solve it. Because personally, I don't think that it is acceptable or viable to continue teaching with this worry of "when is a student next going to ask me to play something?"! I work on it everyday, using meditation, affirmations and creative visualisation and I sight read a lot everyday and play through as much music as I can get my hands on, just as I would tell my students to do, but I am doing it for confidence, rather than to improve my skills. I am also pushing myself to accept every challenge/opportunity to play in front of people. This is easier to start with in front of my little 6 and 7 year old students, because I don't feel that they are going to judge my playing, they are just going to enjoy the music and the fact that it is
me playing the piano
for them.
I'm sorry that this has been a huge post, but I completely empathise with your situation and just wanted to suggest some ways to deal with the problem. Hopefully you will be able to overcome it, as I am trying to do. In terms of the immediate future with this student, I would spend as much time as possible this week practising that grade 7 piece, and play it to someone (partner/children/friend) so you have something to show him next time and are slightly more prepared.
C x
P.S. - My teacher is a brilliant pianist, regularly performs in public and I have heard her play many times - I know her well and she doesn't have stagefright in the slightest (so envious of her!). But she doesn't like playing her own pieces (rather than exam pieces) in lessons and at student recitals for a different reason: She always wants to perform beautifully and says that she finds it hard to mix business/work with personal performance/piano playing. She feels that she can't switch her head between the two different types of playing, so either her performance would be compromised or she wouldn't be able to concentrate on teaching the lesson.