When a prescription is presented to the pharmacist to be data entered into the computer for on hold purposes, it is entered with the same "accuracy" as a prescription that is to be filled at that moment.  It is then assigned a prescription number and placed in hard copy files with other prescriptions. Most computer systems now have scanning capability so that when an on hold prescription request is made, whatever the date, the scanned copy of the original hard copy prescription can be reviewed by the pharmacist at any point in time.  To "renew" an on hold prescription for the sole purpose of getting it in chronologic order makes no sense, uses valuable time and increases the opportunity for errors.  

The original on hold prescription is assigned a number and can be retrieved anyway.  I cannot see any advantages for having to "renew" on hold prescriptions, but I can see plenty of disadvantages.