Have you had multiple LDs in which you've woken up straight away, or have you only had your first so far?

If you've only had one, that could be just a first-LD problem. In my first lucid dream, I got that "rush" of becoming lucid, which caused the dream to become unstable; I woke up about 10-20 seconds later. In my next one, I didn't get that same rush of excitement; it was more like, "Oh, cool, I'm dreaming." It was a pretty stable dream, lasting perhaps a couple minutes before I got bored (from a lack of control over the dream environment, as well as not being able to remember my goals) and decided to wake up.

So, yes, if it's just your first, that issue probably won't arise next time.