I occasionally have lucid "false awakening" dreams (the most recent occasion being this past night) where I know I'm dreaming, I have the conscious will to wake up, and when I attempt to wake up it seems as though I've succeeded, yet I remain dreaming.
After the false awakening, I spend time attempting to establish that I am awake (always with the strong expectation that this hypothesis is true). Either in the course of this analysis, or in a subsequent attempt to "go about my business", I shortly become aware that I'm still dreaming, I again attempt to wake up, and the process repeats itself (in some instances, such as the most recent, well over 20 times).
The process is frustrating and upsetting, although I wouldn't characterize it as a nightmare.
My question is whether there's a term or expression for this particular kind of lucid dreaming, perhaps from the scientific study of dreaming, or from mythology/antiquity, or from a pop culture reference to a story where "inability to wake from a dream" features prominently as a plot device?