I am bringing my father to the UK from South Africa for a 6 month holiday. During that time I would like to take him on a small holiday in Europe. Can he do this on his visa or would he need a new visa to reenter the U.K.?
The visa will have a "number of entries" field. This normally says "MULT," which means the visa is valid for multiple entries. If his visa says this, then yes, if you take him to the continent, he will not require a new visa to return to the UK.
If the visa has a number in this field, then you must count the number of entries allowed and be careful not to exceed it. If the value is 1, then once he leaves the UK, he'll need a new visa to enter again. If there is a 2, then he could take a single trip to the continent and return to the UK without needing a new visa.
The controlling reference for this is found in Paragraph 25A of the Immigration Rules.
The UK government has a nice picture at https://assets.publishing.service.gov.uk/government/uploads/system/uploads/image_data/file/23572/s300_vignette.jpg.