Will the same thing happen to the promise of extended longevity as happened to the space program in the past half century - an early push, and then lack of interest and stagnation? I don't think that this is a likely model, due to the very different institutions and costs. It is comparatively cheap to contribute to progress in medicine, and many groups have the ability to do so usefully at this time.
Nonetheless, this is one of the nagging fears that motivates us to action - that present public disinterest in enhanced longevity will spread to the medical community, rather than giving way in the face of clear signs of progress and benefits emerging from the lab. That no new groups will arise to carry forward the torch of progress.
Again, I don't think that this is as plausible as a future of continued progress. But will that progress be fast enough to help us? That depends on what we do - progress only happens when it is made to happen. We build the future. If you want something done, you have to work on it:
My greatest fear about the future is not of technology running out of control or posing existential risks to humankind. Rather, my greatest fear is that, in the year 2045, I will be 58 years old and already marked by notable signs of senescence, sitting at the kitchen table, drinking my morning coffee, and wondering, "What happened to that Singularity we were promised by now? Why did it not come to pass? Why does the world of 2045 look pretty much like the world of 2013, with only a few cosmetic differences?" My greatest fear is that, as I stare into that mug of coffee, I would recognize that it will all be downhill from there, especially as "kids these days" would pay no more attention to technological progress and life-extension possibilities than their predecessors did.
My greatest fear is that they would consider me a quixotic old man, fantasizing about a future that never was, while they struggle to make ends meet in an ever-more hostile economy (which would look much like our own, except farther along in the sequence of gradual decay, because nobody cares), strangled by labyrinthine restrictions arising out of Luddism and change-aversion within the widespread society. In short, my greatest fear is that our present will be our future, except that I and the present generation of longevity activists will lose our youthful vitality and will ourselves be rapidly approaching the abyss of oblivion.