Bruce Moen has written a number of books about his experiences. He learned a form of AP via the Monroe Institute.
He discusses two modes of reacting to his experiences. In mode of thought he was the Perceiver, taking in the experience. In another mode of thought he was the Interpreter, making associations and ‘thinking’ about his experience.
He found that often the ‘Interpreter’ would cut in, and disrupt his experience. Focussing more on the ‘Perceiver’ helped him stay involved in the experience.
I think a similar approach can help extend a lucid dream. Too many of my dreams end abruptly when I get caught up in analysing what is going on.
A related technique is when you become lucid, take time to slowly look around, feel the environment, look at your hands. All of these are encouraging ‘perception’.
On the other hand, if you lose lucidity rapidly, you may need to focus more on the Interpreter. Ask yourself some questions. Interview a DC!