How mental health problems can affect sleep. There are number of different ways that a mental health problem can have an impact on your sleep. For example: 1  Stress and anxiety can cause you to have thoughts racing through your mind, making it difficult for you to sleep.leep problems can lead to any of the following: 1  Struggling to deal with everyday life – tiredness reduces your ability to deal with difficult situations as well as the challenges of day-to-day life. 2  This may lower your self-esteem, make it harder to cope and cause your mental health to deteriorate.