First, a few questions about Dad - is he independent, or do you or someone else provide some care for him? Does he have other health issues - many can be tied to increased fall risk. Has he had a recent illness or hospitalization? Is Dad generally active, or very sedentary - he may be getting week.

If my Dad was having this issue, here are the steps I would suggest to him (or arrange for him) -
A physical with standing/sitting/reclining blood pressure checks, blood chemistry to rule out anemia, electrolyte imbalances, a silent infection or other correctible causes and a balance check.
A review of his medications to see if any increase risk of dizziness of falls (a trained RN or clinical pharmacist is best for this task.)
If these seem normal, some strength and balance training with a physical therapist - they can sometimes spot other issues and report them to the doctor.
Hearing and vision checks if he hasn't had them recently.
A neurology consult if the above checks don't give the answer.

Does this give you a starting place?