Some natural phenomena will remain unexplainable not necessarily because science has not found an answer but because it may never find one.
Here, a few examples:
Size of the Universe:
Not much is known of the actual size of the Universe, we live in a part of the Universe we can observe; hence the term "the observable Universe", the finite speed of light means, a distant enough object will remain invisible to us forever.
Furthermore, the expansion and acceleration of the Space will make certain that even if travel at light speed were ever possible, we still could not travel far enough to learn all we can about our Universe or how large it truly is.
End of the Universe:
There isn't a consensus and probably no way of reaching one as to how the Universe ends, several models have been proposed, but these are speculative and not one of which is better than another.
Proposals include a scenario where all stars inexorably burn out, and the universe cools down, and all activity ceases.
In another, Space accelerate and stretches out maximally and is ripped.
Another is a scenario where the universe expands to a point where the strength of the expansion weakens, and then gravity causes the entire mass of the universe to race back towards a centre, this would lead to everything being crushed into an infinitesimal point, thereafter which it explodes and expands like at the big bang, in this scenario it is suggested this cycle repeats several times over.
Gravity:
Gravity is one of the fundamental forces of nature and one that we most readily interact with and are aware of, but for its commonality, it is one of the biggest mysteries in science.
The volume of emphasis and research on it has brought us no closer to understanding what it is, we know what it does, how it behaves, but we do not know what it is in a fundamental way, although my guess is we might actually eventually figure this one out.
The Big Bang:
The big bang as an event is fundamental to cosmology, it is key to our understanding the history, present and future of the universe, but as it turns out, the farther back into that event we go, the less we understand the physics and the less our understanding of the laws of physics apply.
The period before the big bang is shrouded in perhaps intractable mystery; so it becomes impossible to assume the nature of anything at this point, as such, questions like where did the substance or energy or interactions come from?! What set it off and what mechanisms if any were involved?! might remain unanswered.
Evidence from observation of the cosmic microwave background radiation while useful for understanding moments after the big bang, can only help us speculate on the very beginnings of the Universe.
Conclusion
These and more like them are examples of questions that present us the unique quality of being perhaps unanswerable, although knowing that may spur the insatiable human mind to seek for answers and reveal more of the mysteries of the universe to us.
Because although we might turn up with nothing, we must exhaust all options and possible answers.
There is much yet to learn about our universe and countless discoveries to be made. Ad Astra.