As a former manager, I look at this from a different point of view. Are you dropping shifts often? What has management already done to accommodate your needs? Have you gotten Human Resources involved as an advocate on your behalf. I ask too what industry you are employed in (for example is it within the service industry where working weekends and evenings is a standard expectation)? How does not showing with little notice affect the rest of the team? How far ahead are shifts scheduled? Were the shifts and hours of employment discussed and made clear as a terms of employment on hire? Is management aware of your problems. I admit that if I were unaware of such a personal issue I wouldn't accept sleep routine as a reason for not showing up to a scheduled shift.

My recommendations are to disclose your mental health issues (by law they cannot hold this accountable). Talk to your manager about your limitations and offer to cooperate with coming to an agreement regarding what will work. Get your EAP involved if you have one. If you are employed in an industry where they cannot schedule you to accommodate your needs it might come to having to find an alternate career choice.

I don't believe we can expect an employer to comply without we ourselves coming to the table.