LJ,
I've worked at the same animal hospital for the past 22 years. We have 10 vets, 2 offices, a large animal facility, perform surgeries and rehabilitation, groom, board and accept referrals from other clinics. In the past 2 weeks we've had 4 people out with Covid (2 doctors), 3 quit (2 without notice), and 1 to 2 doctors out a week either at conferences or on vacation. Add in the multiple emergencies (often up to 10 a day plus overnight) to an already full schedule and you get a picture of a typical day at a vet practice. 

It is not unreasonable for your vet to request at least 24 hours notice for prescription refills. This allows them to focus on the immediate needs of the patients in front of them and address prescriptions as time allows in between appointments. 
Vets everywhere are struggling with staffing and other issues, trying to do the best they can. It was nice of your pharmacy to reach out to the vet about your prescription. If you're not satisfied with the service that you'd been receiving, then perhaps you will be happier with another facility.
--
Jennifer in Middle TN  2010
 Mill 33 1/3 yrs Arabian-PPID, IR & Pacemaker Dependent; 2-13-89 to 6-11-22
Jack 23 yrs TN Walker- IR & RAO

https://ecir.groups.io/g/CaseHistory/files/Jennifer%20and%20Millionairess

https://ecir.groups.io/g/CaseHistory/album?id=831

https://ecir.groups.io/g/CaseHistory/files/Jennifer%20and%20Jack-TN%20Walker