I had this problem and couldn't find a real solution.
All I could do was save at the beginning of my work day, open a new case, and power through until I had enough clues for an APB. If the suspect wasn't on site I would restart the day.
Alternatively you can quit and rejoin the force, but you lose a promotion.
Fortunately you only need 6 solved cases to get promoted to the top of the career, and they carry over even if you quit and rejoin the force to reset your case.
After solving 6 cases, I pushed papers all the way to the top!