Inexplicable and unresolved events can be greatly used in hard science fiction in order to show the approaches how people attempt to study them.
A truly hard sci-fi might not even provide the solution of this inexplicable event as the resolution of the story: the mystery might still remain a mystery, because that was not the point of the story. The point of the story was to analyze the approaches the researchers made and highlight their flaws.
Stanisław Lem was a master of this approach. Many of his hardest sci-fi novels have an inexplicable mystery which stays completely unresolved even when the story is finished.
- His Master's Voice: SETI records a signal from space which looks like a massagemessage sent by extraterrestrials.
By the time the project is ended, they are no more sure than they were in the beginning about whether the signal was a message from intelligent beings that humanity failed to decipher, or a poorly understood natural phenomenon.
- Fiasko: Signs of possible extraterrestrial intelligence are found on an exoplanet, and an expedition is sent to make contact with them.
As the title suggests, they fail. They arrive to the planet, and it is indeed inhabited by intelligent life, but they are so different from us, that every attempt at communication fails. Due to one of the explorers botching up, we don't even get to know how they look like and what they really are.
- Katar: In a holiday resort, a series of mysterious deaths occur, with very strong correlations between the profiles of the victims, hinting towards a serial killer.
At the end it seems highly likely that it was just a coincidence, and the deaths happened purely by chance.
- Solaris: One of the most famous novels of the author involves the study of a planet which is covered by a seemingly intelligent ooze.
The researchers painstakingly catalogue all the phenomena they can observe, but they find no conclusions and no information about what they are, what they mean, and they fail at every attempt to communicate with it.