Yes, the amount your father pays for nursing services while he is incapacitated and requires round-the-clock care can be included in figuring his medical expense deduction. The following explanation is taken from IRS Pub. 502 Medical and Dental Expenses.

"Nursing Services

You can include in medical expenses wages and other amounts you pay for nursing services. The services need not be performed by a nurse as long as the services are of a kind generally performed by a nurse. This includes services connected with caring for the patient's condition, such as giving medication or changing dressings, as well as bathing and grooming the patient. These services can be provided in your home or another care facility.

Generally, only the amount spent for nursing services is a medical expense. If the attendant also provides personal and household services, amounts paid to the attendant must be divided between the time spent performing household and personal services and the time spent for nursing services. For example, because of your medical condition you pay a visiting nurse $300 per week for medical and household services. She spends 10% of her time doing household services such as washing dishes and laundry. You can include only $270 per week as medical expenses. The $30 (10% × $300) allocated to household services can't be included. However, certain maintenance or personal care services provided for qualified long-term care can be included in medical expenses. [See Maintenance and personal care services under Long­Term Care, earlier.] Additionally, certain expenses for household services or for the care of a qualifying individual incurred to allow you to work may qualify for the child and dependent care credit. See IRS Pub. 503 Child and Dependent Care Expenses.

You can also include in medical expenses part of the amount you pay for that attendant's meals. Divide the food expense among the household members to find the cost of the attendant's food. Then divide that cost in the same manner as in the preceding paragraph. If you had to pay additional amounts for household upkeep because of the attendant, you can include the extra amounts with your medical expenses. This includes extra rent or utilities you pay because you moved to a larger apartment to provide space for the attendant."

With regard to your question about nonprofit organizations: This status is granted by the IRS to organizations that serve the public good; such status is never granted to an individual. I am uncertain as to what perceived benefit this would hold for your father. NPOs are still subject to the same regulations as any other entity as employers, including liability for FICA taxes on wages.