Science has a self-imposed limit: we restrict ourselves to the Scientific Method. So, we only study nature, and cannot study the questions that are basic to religion.
Another limit is that sometimes, evidence is unobtainable. In the specific case of evolution, the most usual problem is that time has erased all but a few hints and clues.
However, there is no convincing argument that any of Evolution's unsolved problems are fundamentally inexplicable by science. And, evolution is a very active area of science. Any list of "unexplained evolututionary problems" which is a few decades old will contain things which are now solved. For example, the origin of the immune system.
Breakthroughs are not just someone having a bright idea - although that happens. Some were simply because a century of hunting finally turned up the crucial thing. For example, conodont teeth were first found in 1856, but a fossil of the animal that had those teeth wasn't found until 1983, 127 years later.
Other breakthroughs were because some other science's advances were co-opted. For example, geneticists learned to read DNA, and it turned out that "junk DNA" contains genetic fossils.
But some of the breakthroughs were just plain unexpected. For example, someone put ground-up tarry material from the Murchison meteorite in water, and it spontaneously formed hollow spheres the size of cells. This sort of discovery can convert a "wildly improbable" historical event into an inevitable historical event. (In this case, the invention of cell walls.)
There's every reason to believe that breakthroughs will continue to happen. So, it's clear that at least some of today's mysteries will be solved.