The fear of losing one's mind often goes hand-in-hand with specific mental health challenges. Panic, anxiety, paranoia, and other symptoms can make a character feel like they're falling into a hole they can never climb out of—which, of course, reinforces the fear. This can become a spiraling catch-22 situation that's hard to escape. As with many fears, some individuals who are afraid of losing their mind will become obsessed with keeping themselves safe from it while others will respond with avoidance and denial about any mental health concerns they may have.

Needing verification or affirmation from others that the character is making the right decisions
Being obsessed with (or obsessively avoiding) people and situations dealing with mental health conditions
Researching various disorders and symptoms
The character rehearsing things they know to be true
Employing grounding techniques (controlled breathing, tapping, repeating a word or phrase, etc.)
Repeatedly asking if they are making sense or speaking logically
Seeking a higher power
Exhibiting other mental and behavioral comorbidities
Overcompensating for perceived weaknesses or deficiencies
Making excuses to avoid social gatherings 
Withdrawing from others
Becoming homebound
The character clinging to the trustworthy people in their life
Seeking (or rejecting) therapy, medication, or other treatments
Insomnia