This is a topic of great interest to me, since I have a lot of trouble with LD stability. Recently, Moonbeam pointed out to me that LD stability means two things:
1) Not waking up too soon.
2) Not losing lucidity.
Maybe that's where the idea of balancing attention that you mentioned comes in. Having an LD is like balancing on top of a narrow wall: if you fall on one side of the wall you wake up whereas if you fall on the other side you end up in a non-lucid dream. The problem (I think) is that LDs are inherently unstable, because being aware that you're dreaming tends to wake you up, while trying to moderate the awareness that you're dreaming can make the awareness go away completely.
One thing I've found that can help with stability is just to consciously think about the problem on a regular basis. Before going to sleep I repeat to myself that when I become lucid I will take various steps to maintain stability. Also, when I do RCs during the day I practice dream-stability exercises. For example, I'll rub my hands together or touch various objects and think about what they feel like.
Moonbeam mentioned that--besides inducing lucidity--the proper use of supplements can maintain stability in the sense of reducing the likelihood that you'll lose lucidity. She also pointed out that taking supplements earlier in the sleep cycle will cause you to have LDs earlier, which will make it less likely that you'll wake up prematurely. I hope she'll post some of her theories on stability here.