I have trouble with stabilization too! I've had 1400+ lucid dreams in 4+ years but I don't think I've ever had any last longer than 10 minutes. Most of my lucid dreams are about 1-3 minutes in length.

I think my stabilization problem stems from me being a light sleeper. It is more difficult for me to stay asleep in general, so it is more difficult for me to stay asleep in order to keep the dream going. My non-lucid dreams have always been fairly short as well. I don't remember having a non-lucid dream lasting more than 20 or 30 minutes.

I've been thinking of approaching stabilization from a physiological perspective. The stabilization technique should involve the things needed to be maintained in order for the dream to be maintained. For example, the stabilization technique should involve staying asleep because we need to be asleep to keep the dream going. It should also involve keeping REM sleep going.

Doing a bit of research, I read that REM sleep activation involves acetylcholine. Acetylcholine plays an important role in arousal, attention, and motivation so these things should be involved in a stabilization technique. I also read that that REM deactivation involves noradrenaline. Noradrenaline is involved during situations of stress or danger so these things should be avoided in a stabilization technique.

It sounds like stabilization of dreams is a matter of keeping the mind motivated while keeping the body asleep. The "Lie down, hold still, and wait" techniques used during WILD are used for this purpose so perhaps mental aspects of them can be used as stabilization techniques during dreams.