Not waking up after achieving lucidity is a bit like not falling off your bike when you remove the training wheels. It can be quite difficult at first, but becomes such a second nature that eventually you don't even have to think about it.

The short version of the answer you want is that lucid dreaming occupies a middle ground between many extremes of consciousness. In this case we are dealing with the continuum between excitement and disinterest. Upon becoming lucid you are immediately on a tightrope with one extreme to your left and the other to your right. Become too excited about being lucid and you will wake up immediately. Become disinterested and you will fall back into normal dreaming... or even worse into deep sleep.

So the trick is to find and maintain the middle ground. Keenly interested detachment, or something to that effect. If you practice meditation in your waking life, this will be much easier to do. I would suggest you stop what you are doing upon achieving lucidity and immediately take a deep breath. If the world around you still seems to want to dissolve, try spinning. For some reason that often can lock you into a dream that would otherwise eject you. Most important is simply to will that you stay dreaming.

You may have to work on distinguishing lucidity from being awake. For many people, the act of recognizing that they are dreaming is synonymous with waking up... and so that is exactly what they do. Next time you find yourself lucid, calm yourself. Relax your mind and then try and recall the things you wanted to do in the lucid state. Then calmly go about doing them.