Will this day ever come?
Well, logically, humanity's gotta bite the dust some day. What's really the issue at hand, i'd imagine, is how
the day will come about, and what goes down when it does.
Will humans live to see the decline of their civilization?
Short answer: duh. Long answer: depending on how you define civilization, there'll be human civilization as long as more than one person exists together. So unless humanity ends with everyone suddenly being alone, or people dying too fast for other's to realize that civilization is going down the tubes, yeah, I think it's inevitable that we will.
Someone, please, tell me I'm wrong.
I can't tell you that your proposed scenario is impossible, but there are certainly other possibilities. I don't know if you're familiar with the idea of technological singularity, but, while it's a debatable alternative, makes for a much happier ending (or at least prolonging) of human civilization. In a nutshell, the idea is that AI will eventually become advanced enough to improve itself without need of human influence, causing a massive jump in technological and computing power (the term "intelligence explosion" kinda makes sense here, really). Potentially, that could lead to the technology we need to utilize our resources efficiently enough that we can feed, educate, house, and all around nurture the masses. Similarly, the possibility of space travel/colonization would provide a more than adequate supply of resources, more or less ending the practical need for any sort of war or conflict between humans. Hell, with enough technology, it's conceivable that we could keep spreading out until the universe collapses in on itself, or another big bang rolls around, or whatever sort of universe-ending-scenario you like hits. Almost like a happy ending!
That alternate ending optimistic enough for you?