Most clinics I meet have a good receptionist. A fair few have had several.
The job, as it usually runs, is to answer every call, greet every patient, chase every form and remember every rebook, all at once. Good people can carry that for a while. Then they burn out or move on, and everything that lived in their head leaves with them. The clinic was running on one person's memory, and memory doesn't scale, particularly the week they're on leave.
Patients slip through for the same reason. Nobody forgets on purpose. The rebook needed someone to notice at the exact moment the phone was ringing, and the phone won.
I saw the same pattern in our own gym. Coaches on the floor, enquiries waiting, and whoever was on the desk trying to hold it all. What changed things was taking the repeatable part of that job off people entirely. The system sends, reminds, follows up and flags, every time, whoever is rostered on. The desk keeps the judgement, and the patient standing in front of it.