If you are an at will employee, your employer can cut your hours or terminate you for any reason or no reason at all provided you are not being targeted based on a protected class such as age, race, disability, etc.
Reading your question it appears you have been hopitalized on more than one occassion and provided your employer with a medical note to substantiate your abscence. Depending upon the number of employees the company has and the nature of your medical problems, you may have qualified for FMLA or CFRA. You might also have a recongizable disability under FEHA. If you qualified for FMLA/CFRA and or have a condition that is recognized as a disability, than the employer may not cut your shifts, as this could be disability discrimination and interference with FMLA/CFRA rights, if it is a qualified employer under these laws. I suggest you contact an experienced employment law attorney, in FMLA/CFRA and FEHA claims, to discuss the matter in greater detail than this forum allows.
The opinion provided herein does not create or constitute an attorney-client relationship. An attorney-client relationship cannot be created without mutual consent of both parties, and only after a face-to-face consultation and an appropriate fee contract has been entered into. Nor should the opinion provided herein be exclusively relied upon, as there are many factors and exceptions within the law which simply cannot be explored fully within this forum and upon the limited information provided. The opinions expressed herein are based solely upon the laws of the State of California. Additionally, you should always consult, in person, a qualified attorney regarding any specific legal problem or matter and not rely on the information provided herein. .