According to legend, when an Etonian was flogged, the cost of the birch was added to the bill sent to his parents at the end of term. If this is true it would suggest that a fresh birch was required on every occasion (and I don’t suppose this was insisted on by the Health and Safety Executive).
My interest in corporal punishment was stimulated by redaing the yellow-jacketed Billy Bunter books at the age of 9 & 10 Mr Quelch and prefects swished their canes regularly but on one or two occasions a boy was publicly birched by the headmaster for a particularly heinous offence. As I recall Frank Richards does not tell us whether such birchings necessitated the removal of trousers.