Have you considered that you aren't getting hard because you are nervous? You are really putting a lot of pressure on yourself. You might as well hit it with a newspaper.
Being with the girl make just make you nervous, too. It can also be difficult to get used to being sexual with another person, at first. If you can't penetrate, maybe have her use her hand on you for a couple of times until you are more comfortable with her.
Are you using condoms (because you should be, right?). Condoms can be a little difficult to get used to. Try masturbating with a condom on to get used to how it feels. That will make it easier when you are with your girlfriend. Also, try not masturbating for a couple of days before you have sex. You may not be excited enough to keep it going.
And yes, if she is a virgin, she may be a little tighter than she otherwise would be, but they don't stretch a lot. Perhaps your aim is a little off due to lack of practice.
Also, if you lose your girlfriend because of this, then she wasn't who you thought she was. If you love someone, it shouldn't matter (especially at first) and you should be able to work things through together. Talk to her about it and I'm sure she will be reassuring. Don't be embarrassed. As you can see, you aren't the only one who has this issue. It won't always be this way, you just have to work through it.
