Hm, I guess that makes sense - certainly nothing obvious leaps out to me when I consider real-world mystery setups other than crime 
Maybe a good place to start is to think of professions where one's job is to discover the truth about something:
- Detectives
- Doctors/Psychologists
- Academics (scientists etc)
I guess a medical professional finding out what a patient is suffering from could make a compelling mystery. Even if it's not some rare and unknown ailment, people with complex symptoms get misdiagnosed all the time, and it's also serious enough to care about ...
Similarly with psychology; people aren't always great at communicating their thoughts and feelings - to understand someone, it's not as simple as taking everything they say at face value. Some people can only bring themselves to talk about their struggles through abstractions or allegory (a la 'asking for a friend'), and it's not always a thinly veiled one-to-one correspondence. Incidentally, (I might not have conveyed it clearly but) that's more like the kind of thing I'm trying to do here:
... it's not actually supposed to be about trying to dig into the love interest's life via stalking and stuff XD You talk to her, and you only get information she willingly gives you, but she doesn't communicate in a straightforward way and you have to really read into it and piece things together in order to understand how she ticks. By 'prying', I meant stuff like asking sensitive questions about her mental health - and if you end up piecing together an inaccurate picture of her feelings/intentions/experiences etc, she's the kind of person who'll just deal with it instead of correcting you and you get a bad ending
The problem with this, I guess, is research. You really don't want to accidentally spread medical misinformation, where as criminology-related misinformation is comparatively harmless? (And why I'm more comfortable writing my psych-mystery as a story between people in a personal relationship rather than therapist and client, so I don't have to deal with diagnoses and stuff and risk screwing up XD) You could avoid this by doing this in a fantasy world and making everything up, but I can definitely see how this is fictionalized far less often than crime viewing things through the 'real-world' angle XD
(EDIT: Ah right, talking about psych-mystery reminded me of this game I played a long time ago where you work at a mental hospital for sentient plushies. It's no longer free but there are still some let's plays of it on YouTube :])
It seems academia has its problems too; now that I think about it, there isn't even often a specific question that you're trying to answer. With crime, it's 'who dun it' and with medicine, it's 'what is this person suffering from, and how can it be treated?' But with science, it's just kind of general discovery, pushing the bounds of human knowledge. You're not looking for anything in particular, you're just looking for more.
Well, people do end up zoning in on specific questions like 'does P=NP?', but to the average person, it's on the level of 'why do the lights at the convenience store come on after hours' in terms of why they should care. These questions are hard to motivate. Again, this could be fantasy-fied with an easier-to-motivate question like 'where does life come from' and a fantastical answer to that question, but again, I can definitely see how this is fictionalized far less often than crime viewing things through the 'real-world' angle
Well that was fun to think about 
Please excuse the wall of text XD
Ah, in a 'fear of the unknown' kind of way? Like mystery => unknown => danger => crime?
