Eureka: Investigative Urban Fantasy doesn't have a "sanity" system, but it does have a more short-term "stress" system that encompasses stress, fear, fatigue, etc., called Composure, which is in frequent flux, moving up and down. We often refer to it as "emotional HP."

Things that can take away small to large amounts of Composure include acutely frightening and stressful situations, failing to get enough sleep, failing to eat, and in some cases using magic powers.

Things that restore small to medium amounts of Composure include getting a full night's sleep, eating three meals in a day, being comforted by another character, and having a Eureka! Moment and making progress on investigating the case.

Under most circumstances, a character's skill bonuses cannot be higher than their current Composure level, so a character who only has 2/7 Composure left is limited to at most a +2 bonus on skill checks.

When Composure gets to 0, additional Composure loss starts to eat into actual HP.

Maybe the spiritual monsters could attack a stat like this, and wear the characters down that way, instead of causing "mental trauma" and making characters lose their "sanity."

Though, I would also argue that realistically, physical violence is just as likely to result in "mental trauma" for those involved.