If I understand you correctly, the usual method of designing a database like this is to have one table for the FIXED details of a patient (Name, Address, Date of Births, Gender etc) and a second table listing all the visits, with the PatientID as the Foreign Key
The main form shows the Patient's main details, and a continuous subform shows all the visits with information like VisitDate, Reason, prescription etc.
There are no limits to the number of visits per patient.
Phil